Method for analyzing thin-film layer structure using spectroscopic ellipsometer

ABSTRACT

With extremely-thin-film and thin-film measurement, models are formed based upon a combination of film thickness, optical constants obtained using the dispersion formula, incident angle, etc., and the model and measured spectrums are fit by BLMC for a single layer of a structure with a certain number of iterations, obtaining information regarding the single layer. With thin-film multi-layer-structure measurement, models are formed for multiple layers of a thin-film multi-layer structure likewise, and fit by BLMC or EBLMC, obtaining information regarding the thin-film multi-layer structure. In either measurement, light is cast onto a thin film on a substrate to be measured while changing the wavelength as a parameter in order to obtain the spectrums ψ E (λ i ) and Δ E (λ i ) for each wavelength λ i , representing the change in polarization between the incident and reflected light. The measured spectrums are fit, obtaining the best model. The results are confirmed and stored, as necessary.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a measurement method forperforming precise measurement of the film thickness, the opticalconstants, and the like, for a thin film or an extremely-thin-film on asubstrate, by analyzing the data acquired from a spectroscopicellipsometer using the Best Local Minimum Calculation (which will bereferred to as “BLMC” hereafter).

[0003] Furthermore, the present invention relates to an analysis methodfor an extremely-thin-film-double-layer structure by analyzing the dataacquired from a spectroscopic ellipsometer using the Extended Best LocalMinimum Calculation (which will be referred to as “EBLMC” hereafter).

[0004] Furthermore, the present invention relates to a analysis methodfor a thin-film-multi-layer structure using a spectroscopicellipsometer. More specifically, the present invention relates to ananalysis method for analyzing the data, which has been acquired from aspectroscopic ellipsometer, with regard to a multi-layer structureformed of unknown materials using the EBLMC as analysis means.

[0005] 2. Description of the Related Art

[0006] (Description of General Background with Regard to a SpectroscopicEllipsometer)

[0007] In general, a spectroscopic ellipsometer has a function whereinpolarized light is cast onto a sample so as to measure the change inpolarization between the incident light and the reflected light. Makingan assumption that the complex refractive indexes of the ambientatmosphere and the substrate are known, the film thickness (d) and thecomplex refractive index (N=n−ik) can be calculated based upon thechange in polarization between the incident light and the reflectedlight (in a case of analyzing a sample formed of only the substrate, thecomplex refractive index (N₀) is calculated). The change in polarization(ρ) is represented by ρ=tan(ψ)exp(iΔ), and is dependent upon parameterssuch as the wavelength (λ), the incident angle (φ), the film thickness,the complex refractive indexes of the film, the substrate, the ambientatmosphere, and the like. The film thickness and the complex refractiveindex of the film of interest are obtained based upon the measuredchange in polarization and the following relationship.

(d, n, k)=F(ρ)=F(ψ(λ,φ), Δ(λ,φ))

[0008] In case of single wavelength ellipsometer, if the incident angleis fixed, only two independent variables of three unknown values of (d,n, k) can be measured, and accordingly, there is the need to fix one ofd, n, and k as a known value. Note that in the event that measurement ismade with multiple incident angles, the number of measured variablesincreases, even if the single wavelength ellipsometer is used. However,measured pairs of (Ψ(φ₁), Δ(φ₁)) corresponding to different incidenceangles (φ), are partly correlated, leading to difficulties in obtainingprecise values of d,,n, and k.

[0009] The measured spectrum measured by spectroscopic ellipsometer(Ψ_(E)(λ_(i)), Δ_(E)(λ_(i))), which represents the change inpolarization due to reflection from single-layer or multi-layer thinfilms formed on a substrate, includes all information with regard to nand k of the aforementioned substrate, and d, n, and k of each layer.However, the single combination of the information with regard to n andk of the aforementioned substrate, and d, n, and k of each layer, cannotbe simply extracted from the aforementioned measured spectra (excludingthe case of semi-infinite substrate). In general, the method forextracting of the aforementioned single combination is referred to as“spectroscopic ellipsometry data analysis”. During this analysis,modeling is performed using the information with regard to n and k ofthe aforementioned substrate, and d, n, and k of each layer. Theinformation regarding to n and k of the substrate and each layerincluded in the model is obtained from reference data (known tabledata), a dispersion formula, or optical constants of a single-layer thinfilm from a similar material.

[0010] The dispersion formula represents the wavelength-dependency ofthe dielectric constant of the material, wherein the dielectric constantε(λ) can be determined in the optical range between near infrared lightand ultraviolet light based upon the atomic structure of the material.Known examples of dispersion formulas include a formula based onclassical physics (a harmonic oscillator), a formula based on quantummechanics, an empirical formula, and the like, which generally includetwo or more parameters. The model is applied to the measured data byadjusting all the unknown values (thickness of each layer, parameters ofthe dispersion formula, volume fractions of material's components, orthe like) included in the aforementioned model. This processing isreferred to as “fitting”, wherein the thickness, parameters ofdispersion formula, the volume fractions, and the like, of each layerare obtained. The complex dielectric constant ε(λ) of the material canbe calculated from the parameters of the dispersion formula, based uponthe fitting results. The relation between the complex dielectricconstant of the material and the complex refractive index is representedby the following expression.

ε(λ)=N ²(λ)

[0011] Now, brief description will be made regarding fitting operationfrequently employed in methods according to the present invention.

[0012] (Description Regarding the Fitting Figure of Merit χ²)

[0013] With the set of N pairs of measured (experimental) data asExp(i=1, 2, and so on through N), and with the set of N pairs of thedata calculated using the model as Mod(i=1, 2, and so on through N),making assumption that error of measurement follows normal distribution,and with the standard deviation as σi, the mean square error (χ²) isrepresented by the expression$\chi^{2} = {\lbrack {1/( {{2N} - P} )} \rbrack {\sum\limits_{i = 1}^{N}{( {{Exp}_{i} - {Mod}_{i}} )^{2}/\sigma_{i}^{2}}}}$

[0014] wherein P represents the number of the parameters. Theaforementioned expression indicates that the smaller χ² is, the betterthe model matches the measured results. Accordingly, the best model canbe selected from multiple models by selecting the model having thesmallest χ².

[0015] In a case of a sample wherein a single film is formed on asubstrate, the change in polarization is proportional to the phase angle(β)×the cross-section area of the beam. The phase angle (β)(Film PhaseThickness) is represented by the following expression.

β=2π(d/λ)(N ² −N _(A) ² sin² φ)^(1/2)

[0016] Making an assumption that the beam's cross section is constant,the change in polarization can be expressed

[0017] Change in polarization ∝ Film thickness (d)×f(N_(A), N₀, N, φ)

[0018] Here, N_(A) denotes the complex refractive index of the ambientatmosphere, No denotes the complex refractive index of the substrate, Ndenotes the complex refractive index of the film, and φ denotes theincident angle. Note that in general, N_(A) denotes the complexrefractive index of the air, and accordingly, N_(A) will be omittedhereafter. In the event that both the film thickness (d) and the complexrefractive index (N) are small, the change in the phase angle (β)exhibits small value, in some cases, leading to difficulty inmeasurement. Specifically, in this case, the film thickness (d) and thecomplex refractive index (N) become strongly correlated.

[0019] Analysis of an extremely-thin-film-multi-layer structure is evenmore problematic, because the strong correlation between the filmthickness (d) and the complex refractive index (N) may occur for eachlayer. In this case, it is difficult to obtain d, n, and k, for eachfilm based upon the measurement results (ψ_(E)(λ_(i)), Δ_(E)(λ_(i)))which represent the change in polarization between the incident lightand the reflected light.

[0020] Furthermore, as can be understood from the aforementionedexpression, the precision of the incident angle affects the change inpolarization. Accordingly, a method for obtaining a precise incidentangle is necessary. That is to say, determination of the preciseincident angle allows the precise determination of the change in thepolarization of reflected light.

[0021] In the present invention, Effective Medium Theory (EMT) is usedto calculate the effective dielectric function of materials, thosedielectric function's wavelength dependence is difficult or impossibleto express, using only one dispersion formula.

[0022] In general, the effective dielectric constant (ε) of the hostmaterial which contains N number of inclusions (guest materials), eachinclusion is big enough to possess it's own dielectric constant, isrepresented by the expression${( {ɛ - ɛ_{h}} )/( {ɛ + {k\quad ɛ_{h}}} )} = {\sum\limits_{j = 1}^{N}{{f_{j}( {ɛ_{j} - ɛ_{h}} )}/( {ɛ_{j} + {k\quad ɛ_{h}}} )}}$

[0023] wherein ε_(h) represents the dielectric constant of the hostmaterial, ε_(j) represents the dielectric constant of the j-th guestmaterial, and k represents a screening factor. Now, let us consider acase in which one cannot distinguish between the host material and theguest material, i.e., a case that materials of comparable amount havebeen mixed. In this case, approximation can be made wherein thedielectric constant of the host material and the effective dielectricconstant of mixed material are the same ε_(h)=ε, therefore ε_(h) in theaforementioned expression is replaced by the effective dielectricconstant ε. The aforementioned approximation is called “BruggemanEffective Medium Approximation”, which will be simply referred to as“EMA” in this specification hereafter. Using the EMA, the effectivedielectric constant ε of a material, wherein three spherical componentsa, b, and c have been uniformly mixed, is obtained by the expression

f _(a)(ε_(a)−ε)/(ε_(a)+2ε)+f _(b)(ε_(b)−ε)/(ε_(b)+2ε)+f_(c)(ε_(c)−ε)/(ε_(c)+2ε)=0

[0024] wherein ε represents the effective dielectric constant which isto be obtained, ε_(a), ε_(b), and ε_(c), represent the dielectricconstants of the spherical components a, b, and c, respectively, andf_(a), f_(b), and f_(c), represent the volume fraction of thecorresponding components. Volume fraction will be referred to as “Vf”,hereafter. Note that f_(a)+f_(b)+f_(c)=1.

[0025] Effective Medium Approximation (EMA) is applicable, if theseparate regions (components) of mixed material are small compared tothe wavelength of light. EMA is used to model thin film on substrate, ifthis film is either microscopically inhomogeneous or discontinuous orformed by several physically mixed materials.

[0026] Now, description will be made regarding a case that the materialsa, b, and c have been mixed. In this case, EMA is used to calculate thedielectric constant of the mixed layer from the volume fractions of eachcomponent and the dielectric constants of corresponding materials a, band c. Dielectric constant of each component can be determined by eitherreference data or dispersion formula. Assuming the mixed layerthickness, model can be built and fitted to the measured data.

[0027] The calculation methods which are referred to as “BLMC (BestLocal Minimum Calculation)” and “EBLMC (Extended Best Local MinimumCalculation) are frequently used in the analysis method according to thepresent invention. In this specification, these calculation methods willbe referred to the abbreviations of “BLMC” and “EBLMC” hereafter.

[0028] BLMC is used for analyzing a single-layer structure. In theanalysis using the BLMC, fitting is made with a predetermined procedurewhile adjusting the initial values of predetermined parameters within acertain range, so as to obtain the best results.

[0029] EBLMC is used for analyzing a multi-layer structure. In theanalysis using the EBLMC, BLMC is repeated for a film of interest whilemaintaining the predetermined kinds of parameters of the other films tomultiple values at and around the medians thereof, and the best resultsare determined as the results obtained with the EBLMC.

SUMMARY OF THE INVENTION

[0030] It is a first object of the present invention to provide anextremely-thin-film measurement method and a thin-film measurementmethod for analyzing the data acquired from a spectroscopicellipsometer, wherein fitting is made with regard to the measured dataacquired from the spectroscopic ellipsometer and simulation spectrumcalculated from a model employing a combination of the film thickness,the complex refractive index of the film, and the like, using the BLMC,thereby determining an extremely-thin-film structure and a thin-filmstructure.

[0031] It is another object of the present invention to provide anextremely-thin-film-double-layer-structure analysis method fordetermining an extremely-thin-film double structure from the measureddata acquired from a spectroscopic ellipsometer, wherein fitting is madewith regard to the measured data acquired from the spectroscopicellipsometer and simulation spectrum calculated from a model employing acombination of the film thickness, the complex refractive index of thefilm, and the like, using the EBLMC.

[0032] It is a further object of the present invention to provide athin-film-multi-layer-structure analysis method for determining athin-film-multi-layer structure from the measured data acquired from aspectroscopic ellipsometer, wherein fitting is made with regard to themeasured data acquired from the spectroscopic ellipsometer andsimulation spectrum calculated from a model employing a combination ofthe film thickness, the complex refractive index of the film, and thelike, using the EBLMC.

[0033] In order to achieve the aforementioned first object, the presentinvention provides an extremely-thin-film measurement and thin-filmmeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer using best-local-minimum-calculation (BLMC),which comprises a spectrum measurement step wherein incident light iscast onto a thin film on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; a stepfor assuming the complex refractive index (N₀, (n₀, k₀)) of thesubstrate, the complex refractive index (N, (n, k)) of the film, basedupon the dispersion formula, a plurality of film thicknesses (d±mΔd)within a plausible range, and a plurality of incident angles (φ±mΔφ)within a plausible range; a step for performing fitting for theparameters of the dispersion formula (DSP) based upon combinations ofthe incident angle and the film thickness; an analyzing step 1A forselecting fitting results (DSP_(best)) obtained based upon a modelformed of a combination of the film thickness (d_(best)) and theincident angle (φ_(best)), which exhibits the minimal difference betweenthe ψ_(M)(λ_(i)) and Δ_(M)(λ_(i)) obtained by the fitting and themeasured ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)); an analyzing step 2A forperforming fitting for the film thickness (d_(best)) and the dispersionformula (DSP_(best)) with the incident angle (φ_(best)) obtained in theanalyzing step 1A being fixed.

[0034] In the analyzing step 1A and analyzing step 2A, the mean squareerror (χ²) may be calculated from the measured values and the fittingresults for each model, and the fitting results which exhibit theminimal mean square error (χ²) are selected.

[0035] In order to achieve the aforementioned first object, the presentinvention provides an extremely-thin-film measurement and thin-filmmeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer using best-local-minimum-calculation (BLMC),which comprises a spectrum measurement step wherein incident light iscast onto a thin film on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(j)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; a stepfor forming models of the film structure, wherein a thin film on asubstrate is formed with microscopic non-uniformity, or is formed of amixture of several materials, with the complex refractive index (N₀,(n₀, k₀)) of the substrate and the complex refractive index (N, (n, k))of the film, assumed based upon several dispersion formulas or referencedata, which are used for Effective Medium Approximation (EMA); a stepfor assuming a plurality of film thicknesses (d±mΔd) within a plausiblerange, a plurality of volume fractions (Vf±mΔVf) within a plausiblerange obtained based upon the dispersion formulas which have beenemployed in forming the models, and a plurality of incident angles(φ±mΔφ) within a plausible range; a step for performing fitting for theparameters of the dispersion formula (DSP) based upon combinations ofthe incident angle, the film thickness, and the volume fraction; ananalyzing step 1A for selecting fitting results (DSP_(best)) obtainedbased upon a model formed of a combination of the film thickness(d_(best)), the incident angle (φ_(best)), and the volume fraction(Vf_(best)), which exhibits the minimal difference between theψ_(M)(λ_(i)) and Δ_(M)(λ_(i)) obtained by the fitting and the measuredψ_(E)(λ_(i)) and Δ_(E)(λ_(i)); and an analyzing step 2A for performingfitting for the film thickness (d_(best)), the volume fraction(Vf_(best)), and the dispersion formula (DSP_(best)) with the incidentangle (φ_(best)) obtained in the analyzing step 1A being fixed.

[0036] In order to achieve the aforementioned first object, the presentinvention provides an extremely-thin-film measurement and thin-filmmeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer using best-local-minimum-calculation (BLMC),which comprises a spectrum measurement step wherein incident light iscast onto a thin film on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; a stepfor assuming a plurality of measurement conditions (Z_(j)) in aplausible range and performing processing from the second step of theaforementioned extremely-thin-film measurement and thin-film measurementmethod for forming models of a film structure, to the second step, foreach (Z_(j)); and an analyzing step 3A for selecting fitting results, ofwhich the parameters of the dispersion formula and the volume fractionare within predetermined ranges, exhibiting the minimal mean squareerror (χ²), from the fitting results obtained based upon the pluralityof measurement conditions (Z_(i)).

[0037] In order to achieve the aforementioned second object, the presentinvention provides an extremely-thin-film double-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer, wherein at first the spectroscopic spectrumsare generally obtained by measuring the extremely-thin-filmdouble-layer-structure using the spectroscopic ellipsometer.

[0038] New analysis method is generally formed with three analyzingstages. In the analyzing stage 1, the initial values are determined byselecting the plurality of models, which is assumed to match an actualsample. In the analyzing stage 2, EBLMC is performed based upon theinitial values obtained in the analyzing stage 1. In the analyzing stage3, the final fitting is performed and the results are confirmed andstored, as necessary.

[0039] In order to achieve the aforementioned second object, the presentinvention provides an extremely-thin-film double-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer, which comprises a spectrum measurement stagewherein incident light is cast onto an extremely-thin-film double-layerstructure on a substrate which is to be measured while changing thewavelength of the incident light as a parameter in order to obtain theψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) foreach wavelength λ_(i), which represent the change in polarizationbetween the incident light and the reflected light; an analyzing stage1B which includes an analyzing step 1B-1 for forming several models ofthe extremely-thin-film double-layer structure on the substrate basedupon the complex refractive index (N₀, (n₀, k₀)) of the substrate, thecomplex refractive indexes (N₁, (n₁, k₁)) and (N₂, (n₂, k₂)) ofmaterials (Mat 1, Mat 2) of the thin films in plausible ranges, and thefilm thicknesses (d₁, d₂) in plausible ranges; an analyzing step 1B-2for performing fitting for the measured spectrums for each model; and ananalyzing step 1B-3 for selecting fitting results (d_(1(best)),d_(2(best))) obtained based upon a model which exhibits the minimal meansquare error (χ²), or a model with the film thicknesses being withinpredetermined ranges, which exhibits the minimal mean square error (χ²),from the fitting results obtained based upon the several models; ananalyzing stage 2B which includes an analyzing step 2B-1 for settinginitial values of a new model to the fitting results obtained in theanalyzing stage 1B; an analyzing step 2B-2 for performing fitting formultiple models with a film-thickness combination as a parameter aroundand at the film-thickness combination (d_(1(best)), d_(2(best))) servingas the median, using BLMC; and an analyzing step 2B-3 for selecting amodel which exhibits the minimal mean square error (χ²), or a model withthe film thicknesses, the parameters of the dispersion formula, and theincident angle, being within predetermined ranges, which exhibits theminimal mean square error (χ²); an analyzing stage 3B which includes ananalyzing step 3B-1 for performing the final fitting based upon thefitting results obtained in the analyzing stage 2B; an analyzing step3B-2 for confirming the fitting results obtained in the analyzing step3B-1; and an analyzing step 3B-3 for storing the obtained fittingresults.

[0040] In the analyzing step 2B-2, fitting may be performed using BLMCfor materials formed of the double-layer structure in order ofuncertainty of the optical constants thereof.

[0041] The aforementioned extremely-thin-film double-layer-structuremeasurement method may further comprise a step for forming multiplemodels with the film thickness obtained in the analyzing step 1B-3, ofwhich the optical constants are more reliable than the other, as aparameter around and at the film thickness obtained in a range of a fewpercents to a few ten percents; a step for performing BLMC described inthe analyzing steps 2B-2 and 2B-3 for the other layer for each model.

[0042] In order to achieve the aforementioned second object, the presentinvention provides an extremely-thin-film double-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer, which comprises a spectrum measurement stagewherein incident light is cast onto an extremely-thin-filmdouble-layer-structure on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; ananalyzing stage 1B which includes an analyzing step 1B-1 for formingseveral models of one of the first and second layers, which is formedwith non-uniformity or non-continuity, or is formed of a mixture ofseveral materials, with the complex refractive index (N₀, (n₀, k₀)) ofthe substrate thereof, the complex refractive indexes (N₁, (n₁, k₁)) and(N₂, (n₂, k₂)) of the materials (Mat 1, Mat 2) forming the thin films inplausible ranges, the volume fractions (Vf₁, Vf₂) in plausible ranges,and the film thicknesses (d₁, d₂) in plausible ranges, using EffectiveMedium Approximation (EMA); an analyzing step 1B-2 for performingfitting for the measured spectrums for each model; and an analyzing step1B-3 for selecting fitting results (d_(1(best)), d_(2(best)),Vf_((best))) obtained based upon a model which exhibits the minimal meansquare error (χ²), or a model with the film thicknesses and the volumefractions being within predetermined ranges, which exhibits the minimalmean square error (χ²), from the fitting results obtained based upon theseveral models; an analyzing stage 2B which includes an analyzing step2B-1 for forming new models with the initial values based upon thefitting results obtained in the analyzing stage 1B, with the filmthickness, wherein the corresponding parameters of the dispersionformula are less known than the other, as a parameter around the valueobtained the analyzing step 1B-3 in a range of (d₁±mΔd₁) or (d₂±mΔd₂),with the film thickness of the other layer as a parameter around thevalue obtained the analyzing step 1B-3 in a range of (d₂±mΔd₂) or(d₁±mΔd₁), and with the volume fraction as a parameter around the valueobtained the analyzing step 1B-3 in a range of (Vf±mΔVf); an analyzingstep 2B-2 for performing BLMC for the parameters of the layer, whereinthe parameters of the dispersion formula are less known than the other,of the models obtained in the analyzing step 2B-1; and an analyzing step2B-3 for selecting a model which exhibits the minimal mean square error(χ²), or a model with the film thicknesses, the parameters of thedispersion formula, and the incident angle, being within predeterminedranges, which exhibits the minimal mean square error (χ²), from thefitting results obtained in the analyzing step 2B-2; an analyzing stage3B which includes an analyzing step 3B-1 for performing fitting for thefilm thicknesses of both thin films, the volume fraction, and theparameters of the dispersion formula, or performing fitting for the filmthicknesses of both thin films and the volume fraction, based upon thefitting results obtained in the analyzing stage 2B; an analyzing step3B-2 for confirming the fitting results obtained in the analyzing step3B-1; and an analyzing step 3B-3 for storing the obtained fittingresults.

[0043] The aforementioned extremely-thin-film double-layer-structuremeasurement method may further comprise a spectrum measurement stagewherein incident light is cast onto an extremely-thin-filmdouble-layer-structure on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; a stepfor assuming a plurality of measurement conditions (Zi) in a plausiblerange and performing processing from the analyzing stage 1B or analyzingstep 2B-1 through 2B-3 of the aforementioned extremely-thin-filmdouble-layer-structure measurement method for each assumed measurementcondition (Zi); and an analyzing step 1B-4 or 2B-4 for selecting fittingresults, which exhibit the minimal mean square error (χ²), or theparameters of the dispersion formula, and the volume fraction, arewithin a predetermined range, and which exhibit the minimal mean squareerror (χ²) which are selected from the fitting results obtained in theanalyzing step.

[0044] In each of the steps for selecting the results which exhibit theleast difference, described in the analyzing stage 1B, 2B, and 3B, themean square error (χ²) may be obtained between the fitting results andthe measured values, and the fitting results which exhibit the minimalmean square error (χ²), or the fitting results, of which the filmthicknesses, the parameters of the dispersion formula, the volumefraction, and the change in the incident angle, are within predeterminedranges, and which exhibit the minimal mean square error (χ²), areselected.

[0045] In order to achieve the aforementioned third object, the presentinvention provides a thin-film triple-layer-structure measurement methodfor analyzing spectroscopic data acquired from a spectroscopicellipsometer, which comprises a spectroscopic measurement phase forobtaining measured data using a spectroscopic ellipsometer; an analyzingphase 1C for forming an initial model of a thin-filmtriple-layer-structure; an analyzing phase 2C which includes ananalyzing stage 2C-1 for determining unknown parameters of the layer ofinterest forming the thin-film triple-layer-structure, using EBLMC; andan analyzing stage 2C-2 for determining parameters of the other layerswith the parameters determined in the analyzing stage 2C-1 being fixed,using EBLMC.

[0046] In order to achieve the aforementioned third object, the presentinvention provides a thin-film triple-layer-structure measurement methodfor analyzing spectroscopic data acquired from a spectroscopicellipsometer, which comprises a spectroscopic measurement phase forobtaining measured data using a spectroscopic ellipsometer; an analyzingphase 1C for forming an initial model of a thin-filmtriple-layer-structure; an analyzing phase 2C which includes ananalyzing stage 2C-1 for determining unknown parameters of the layer ofinterest forming the thin-film triple-layer-structure, using EBLMC; andan analyzing stage 2C-2 for determining parameters of the other layerswith the parameters determined in the analyzing stage 2C-1 being fixed,using EBLMC; an analyzing phase 3C which includes an analyzing stage3C-1 for performing the final fitting for the model obtained in theanalyzing phase 2C; an analyzing stage 3C-2 for confirming the fittingresults obtained in the analyzing stage 3C-1; and an analyzing stage3C-3 for storing the fitting results obtained in the analyzing stage3C-2.

[0047] In order to achieve the aforementioned third object, the presentinvention provides a thin-film n-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometer,which comprises a spectroscopic measurement phase for obtaining measureddata using a spectroscopic ellipsometer; an analyzing phase 1C forforming an initial model of a thin-film n-layer-structure; and ananalyzing phase 2C for determining unknown parameters of the layer ofinterest forming the n-layer structure based upon the initial modelwhich represents the thin-film n-layer-structure, using EBLMC.

[0048] In order to achieve the aforementioned third object, thin-filmn-layer-structure measurement method for analyzing spectroscopic dataacquired from a spectroscopic ellipsometer, which comprises aspectroscopic measurement phase for obtaining measured data using aspectroscopic ellipsometer; an analyzing phase 1C for forming an initialmodel of a thin-film n-layer-structure; an analyzing phase 2C fordetermining unknown parameters of the layer of interest forming then-layer structure based upon the initial model, using EBLMC; ananalyzing phase 3C which includes an analyzing stage 3C-1 for performingthe final fitting for the model obtained in the analyzing phase 2C; ananalyzing stage 3C-2 for confirming the fitting results obtained in theanalyzing stage 3C-1; and an analyzing stage 3C-3 for storing thefitting results obtained in the analyzing stage 3C-2.

[0049] Analysis may be made with unknown parameters as the filmthicknesses, the optical constants of unknown materials or the volumefractions.

[0050] The spectroscopic measurement phase may include a spectrummeasurement step wherein incident light is cast onto a thin-filmtriple-layer structure or a thin-film multi-layer structure on asubstrate which is to be measured while changing the wavelength of theincident light as a parameter in order to obtain the IPE and Δ_(E)spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) for each wavelengthλ_(i), which represent the change in polarization between the incidentlight and the reflected light; and a storage step for storing the dataobtained in the measured step.

[0051] In the analyzing phase 1C, the single Best First ApproximationModel (which will be referred to as “BFAM” hereafter) may be selectedfrom a plurality of models by fitting, or a model is assumed based uponknown data, as the initial model, and wherein in a case of employing theBFAM, the analyzing phase 1C which includes an analyzing step 1C-1 forforming a plurality of models within a plausible range; an analyzingstep 1C-2 for performing fitting with regard to the film thicknesses,the volume fractions, and the incident angles, based upon the pluralityof models; and an analyzing step 1C-3 for selecting a model whichexhibit the minimal mean square error (χ²), or a model, of which thefilm thicknesses, the volume fractions, and the incident angles, arewithin predetermined ranges, and which exhibit the minimal mean squareerror (χ²), from the fitting results obtained in the analyzing step1C-2.

[0052] The analyzing stage 2C-1 may include an analyzing step 2C-1-1 forreplacing the optical constants of the layer of interest with a singledispersion formula, which is the least known in the thin-filmtriple-layer structure or thin-film n-layer structure, in the determinedinitial model; an analyzing step 2C-1-2 for forming a plurality ofmodels based upon the initial model with the film thicknesses, thevolume fractions, or the like, of desired layers other than the layer ofinterest (the number of layers is 1 through (n−1)), as parameters;performing EBLMC for the layer of interest based upon each model; ananalyzing step 2C-1-3 for selecting a model which exhibit the minimalmean square error (χ²), or a model, of which the film thicknesses, thevolume fractions, the parameters of the dispersion formula, and theincident angle, are within predetermined ranges, and which exhibit theminimal mean square error (χ²), from the fitting results using EBLMC,obtained in the analyzing step 2C-1-2.

[0053] In each of analyzing stages 2C-2 through 2C-t, the same steps asthe analyzing step 2C-1-1 through analyzing step 2C-1-3 described in theaforementioned thin-film triple-layer-structure measurement or thin-filmmulti-layer-structure measurement method may be performed, making anassumption that the optical constants of the layer of interest obtainedin the previous stage are almost known.

[0054] In the analyzing phase 2C, EBLMC may be performed for thematerials forming the triple-layer structure or n-layer structure inorder of uncertainty of the optical constants of the materials, andwherein the EBLMC is performed for at least one to t times, regardlessof the number of the layers in the structure.

[0055] In the analyzing phase 2C, in the event that the fitting resultswith the minimal mean square error (χ²) do not exhibit the filmthicknesses, the parameters of the dispersion formula, the volumefractions, and the incident angle, within predetermined ranges, theanalyzing phase 2C may be repeated with a certain number of iterations.

[0056] In the analyzing phase 3C, the final fitting may be performed fordesired parameters of the model obtained the analyzing phase 2C,confirmation is made for the fitting results obtained in the finalfitting, and the fitting results are stored.

[0057] In the event that confirmation is made in the analyzing step 3C-2that the fitting results with the minimal mean square error (χ²)obtained in the analyzing step 3C-1 may not be within predeterminedranges, the flow returns to the analyzing phase 1C, and analysis is madeagain.

[0058] The analyzing stage 2C-1 may include an analyzing step 2C-1-1wherein in the event that the layer of interest cannot be represented bya single dispersion formula in the same way as the aforementionedthin-film triple-layer-structure measurement or thin-filmmulti-layer-structure measurement method, Effective Medium Approximation(EMA) is performed making an assumption that the layer of interest isformed of a mixture of several materials, and at least one materialforming the layer of interest is represented by a dispersion formula; ananalyzing step 2C-1-2 for forming multiple models with film thicknessesor volume fractions of desired layers 1 through (n−1) (n denotes thenumber of layers of the structure) other than the layer of interest, asparameters and performing EBLMC for the layer of interest for each modelwhile changing the volume fraction thereof as a parameter.

[0059] The aforementioned thin-film triple-layer-structure measurementor thin-film multi-layer-structure measurement method may furthercomprise a spectroscopic measurement phase wherein incident light iscast onto a triple-layer-structure or multi-layer-structure on asubstrate which is to be measured while changing the wavelength of theincident light as a parameter in order to obtain the ψ_(E) and Δ_(E)spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) for each wavelengthλ_(i), which represent the change in polarization between the incidentlight and the reflected light; an analyzing step for assuming aplurality of measurement conditions (Zi) in a plausible range andperforming processing from the analyzing step 1C or analyzing step 1C-1through 2C-t-3 for each assumed measurement condition (Zi); and ananalyzing step 1C-4 or 2C-t-4 for selecting fitting results, whichexhibit the minimal mean square error (χ²), or the parameters of thedispersion formula, the volume fraction, and the incident angle, arewithin a predetermined range, and which exhibit the minimal mean squareerror (χ²) which are selected from the fitting results obtained in theanalyzing step.

[0060] In each of the steps for selecting the results which exhibit theleast difference, described in the analyzing phases 1C, 2C, and 3C, themean square error (χ²) may be obtained between the fitting results andthe measured values, and the fitting results which exhibit the minimalmean square error (χ²), or the fitting results, of which the filmthicknesses, the parameters of the dispersion formula, the volumefraction, and the change in the incident angle, are within predeterminedranges, and which exhibit the minimal mean square error (χ²), areselected.

[0061] As described above in detail, the present invention provides anexcellent analysis method for analyzing a thin-film layer structurebased upon spectroscopic data acquired from a spectroscopicellipsometer, thereby enabling precise measurement of the properties ofa thin film such as the film thickness, the volume fraction, and theoptical constants thereof in the semiconductor manufacturing field.

BRIEF DESCRIPTION OF THE DRAWINGS

[0062]FIG. 1 is a block diagram which shows a configuration of aspectroscopic ellipsometer for acquiring spectroscopic measured data,employed in step 10 in an extremely-thin-film measurement method and athin-film measurement method according to the present invention;

[0063]FIG. 2 is a flowchart for describing an extremely-thin-filmmeasurement method and a thin-film measurement method according to thepresent invention;

[0064]FIG. 3 is a schematic diagram which shows a configuration of anellipsometer employed in an extremely-thin-film double-layer-structuremeasurement method according to the present invention, wherein a part ofa sample which is to be measured is enlarged;

[0065]FIG. 4 is a flowchart which shows an extremely-thin-filmdouble-layer-structure measurement method according to an embodiment ofthe present invention;

[0066]FIG. 5 is an explanatory diagram for describing an analyzing stage1B of the aforementioned embodiment in detail;

[0067]FIG. 6 is an explanatory diagram for describing an analyzing stage2B of the aforementioned embodiment in detail;

[0068]FIG. 7 is an explanatory diagram for describing an analyzing stage3B of the aforementioned embodiment in detail;

[0069]FIG. 8 is a schematic diagram which shows a configuration of anellipsometer employed in an extremely-thin-film multi-layer-structuremeasurement method according to an embodiment of the present invention,wherein a part of the sample which is to be measured is enlarged;

[0070]FIG. 9 is a flowchart which shows an extremely-thin-filmtriple-layer-structure measurement method according to an embodiment ofthe present invention;

[0071]FIG. 10 is an explanatory diagram for describing an analyzingphase 1C of the aforementioned embodiment in detail;

[0072]FIG. 11 is an explanatory diagram for describing an analyzingphase 2B stage 1 (stage 2B-1) of the aforementioned embodiment indetail;

[0073]FIG. 12 is an explanatory diagram for describing an analyzingphase 2B stage 2 (stage 2B-2) of the aforementioned embodiment indetail;

[0074]FIG. 13 is an explanatory diagram for describing an analyzingphase 3B of the aforementioned embodiment in detail;

[0075]FIG. 14 is an explanatory diagram for describing a part of ananalyzing phase 2B stage 1 step 2 (step 2B-1-2) of the aforementionedembodiment in detail; and

[0076]FIG. 15 is a flowchart for describing a thin-filmn-layer-structure measurement method, which is a generalized arrangementaccording to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0077] (Description Regarding an Extremely-Thin-Film Measurement Methodand a Thin-Film Measurement Method According to Embodiments of thePresent Invention)

[0078] Description will be made regarding embodiments according to thepresent invention with reference to the drawings and the like.

[0079]FIG. 1 is a block diagram which shows a configuration of anellipsometer used in an extremely-thin-film measurement method and athin film measurement method according to the present invention. Thespectroscopic ellipsometer shown in the block diagram performs aspectroscopic measurement step 10 to obtain the measured spectroscopicdata described later.

[0080] A Xe lamp 1 is a so-called white light source for emitting lightcontaining a great number of wavelength components. The light emittedfrom the Xe lamp 1 is introduced to a polarizer 3 through an opticalfiber 2. The light polarized by the polarizer 3 is cast onto the surfaceof a sample 4 which is to be measured with a predetermined incidentangle (e.g., φ=75°). The reflected light from the sample 4 is introducedto an analyzer 6 through a photo-elastic modulator (PEM) 5. Thereflected light is subjected to phase modulation with a frequency of 50kHz by the photo-elastic modulator (PEM) 5. As a result the polarizationof the reflected light, which is originated from the linearly polarizedincident light, will change periodically from linearly to elliptically.Accordingly, Ψ and Δ can be determined within several msec. The outputfrom the analyzer 6 is connected to a spectroscope 8 through an opticalfiber 7. The output data from the spectroscope 8 is acquired by a dataacquisition unit 9, whereby the spectroscopic measurement step 10 toobtain the measured spectroscopic data ends. Note that the PEM 5 may besituated in front of the polarizer 3 or the analyzer 6.

[0081] It is assumed that the model is preferably modified by adjustingthe incident angle φ₀, rather than fixing the model to a model with thenominal incident angle φ₀ shown in FIG. 1, due to slight non-uniformityof the surface of the sample. That is to say, it is assumed that theaforementioned ψ_(E) and Δ_(E) have been measured under an incidentangle slightly deviated from the nominal incident angle.

[0082] With the actual thin-film measurement method using theaforementioned spectroscopic ellipsometer, analysis is made as follows.First, with the nominal incident angle used in the aforementioned ψ_(E),Δ_(E) spectrum measurement step as φ₀, in the aforementioned ψ_(M),Δ_(M) model simulation spectrum calculation step, the simulationspectrums ψ_(M0)(λ_(i)) and Δ_(M0)(λ_(i)) are calculated with thenominal incident angle φ₀, and the simulation spectrums ψ_(Mk)(λ_(i))and Δ_(Mk)(λ_(i)) are calculated with an incident angle φ_(k) near thenominal incident angle φ₀. Subsequently, the above-describedmodel-simulation spectrums are calculated in block 21, and are comparedto the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) acquired from the spectroscopicellipsometer.

[0083]FIG. 2 is a flowchart which shows a thin-film measurement methodaccording to a first embodiment of the present invention.

[0084] (Block 10)

[0085] Measurement is made using the apparatus shown in FIG. 1.

[0086] (Block 20)

[0087] In this step, the spectroscopic measurement data is processedinto the data in a format which can be compared with the simulatedresults. More specifically, the spectroscopic measurement data acquiredin the aforementioned acquisition block 10 for acquiring thespectroscopic measurement data is converted into the data in the formatof ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)), and the converted data is stored.

[0088] (Block 21)

[0089] In block 21, modeling is made for the sample which is to bemeasured with spectroscopic ellipsometry. Specifically, modeling is madefor the sample which is to be measured, based upon the conditions at thetime of the manufacturing process and the like. Note that modeling ismade for the same sample as in block 20.

[0090] The aforementioned modeling is made with multiple filmthicknesses within a plausible range (d±mΔd), with the dispersionformula assumed based upon the material forming the layer on thesubstrate, and with multiple incident angles within a plausible range(φ±mΔφ).

[0091] With the present embodiment, a great number of models are formedwith a Si substrate, with a first SiO_(x) layer thickness of 20 Å, 25521 , and 30 Å, and with the measurement incident angle of 75.00° to75.05° in increments of 0.01°.

[0092] (Block 22)

[0093] In the processing shown in block 22, the ψ_(M) and Δ_(M)calculated based upon the aforementioned models, and the measurementdata ψ_(E) and Δ_(E) are displayed.

[0094] (Block 23)

[0095] Fitting is made for each model.

[0096] (Block 24)

[0097] Fitting results for the dispersion formula are displayed for eachmodel. The fitting results with regard to the parameters (ε_(s), ω_(t))of the dispersion formula (DSP) calculated with the SiO_(x) filmthicknesses of 20 Å, 25 Å, and 30 Å, are shown in blocks 24 a, 24 b, and24 c, with the incident angle as a parameter.

[0098] (Block 25)

[0099] In block 25, a single combination of the incident angle and thefilm thickness is selected. Note that the selection will be referred toas “first-stage fitting” hereafter. In this example, the first-stagefitting is made as follows. First, let us consider a case of the fittingresults with the film thickness of 20 Å shown in block 24 a. In thiscase, the fitting results obtained with the incident angle of 75.02°exhibit the minimal χ² value of 0.0315 (see block 24 d). Next, in a caseof the fitting results with the film thickness of 25 Å shown in block 24b, the fitting results obtained with the incident angle of 75.03°exhibit the minimal χ² value of 0.0242 (see block 24 e). On the otherhand, in a case of the fitting results with the film thickness of 30 Åshown in block 24 c, the fitting results obtained with the incidentangle of 75.04° exhibit the minimal χ² value of 0.0297 (see the block 24f). In this case, the model (φ_(best)=75.03°, d_(best)=25 Å) shown inblock 24 e which exhibits the minimal χ² value of 0.0242 is selectedfrom these three models.

[0100] (Block 26)

[0101] In block 26, fitting is made with regard to the aforementionedfilm thickness (d_(best)) and the parameters (ε_(s), ω_(t)) of thedispersion formula with the incident angle (φ_(best)) selected in theaforementioned first-stage fitting as a fixed value. In this example,fitting is made with regard to the film thickness (d_(best)) and theparameters of the dispersion formula (ε_(s), ω_(t)), with the filmthickness (d_(best)) of 25 Å as an initial value, with the parameters ofthe dispersion formula of (ε_(s), ω_(t))=(2.00, 12.58) as initialvalues, and with the incident angle (φ_(best)) of 75.03° as a fixedvalue. Thus, second-stage fitting is completed.

[0102] (Block 27)

[0103] The fitting results in the aforementioned second-stage fittingare shown in block 27. In this example, the film thickness d of 24.24 Å,and the parameters (ε_(s), ω_(t)) of the dispersion formula of (2.09,13.24) are obtained as the final fitting results.

[0104] (Block 28)

[0105] The data calculated in the step described in the aforementionedblock 27 is stored.

[0106] (Block 29)

[0107] Confirmation is made that the aforementioned stored data isplausible from the perspective of physics. The fitting results obtainedin the aforementioned first-stage or second-stage fitting step may beunrealistic from both the physical and empirical perspective. In thiscase, determination is made that flawed models have been used, andmodification of models, such as addition or changing of the materialforming the models, is made, and fitting is made again using themodified models. The confirmation is made in block 22, block 25, andblock 27, and in the event that determination is made that the fittingresults are impossible from the perspective of physics, the flow returnsto block 21, as shown in FIG. 2.

[0108] Next, description will be made regarding an implemented exampleof an extremely-thin-film measurement method and a thin-film measurementmethod for measuring a film on a substrate, having a non-uniform ornon-continuous structure, or formed of a mixture of multiple materials,based upon the data acquired from the spectroscopic ellipsometer usingthe BLMC.

[0109] In the implemented example, measurement is made for a film formedof SiO₂ and SiN_(x) (mixture layer SiON) on a Si substrate.

[0110] (Measurement Step)

[0111] In the measurement step, incident light is cast onto theaforementioned thin film (mixture layer of SiO₂ and SiN_(x)) on thesubstrate which is to be measured while changing the wavelength of theincident light as a parameter, in order to obtain measured spectrumsψ_(E)(λ_(i)) and Δ_(E)(λ_(i)), which represent the change inpolarization between the incident light and the reflected light, foreach wavelength λ_(i). Measurement is made using the same measurementapparatus as described above.

[0112] (Step for Forming Models)

[0113] In this step, models are formed for representing a mixture layerformed of SiO₂ and SiN_(x), serving as a thin film on the substrate.

[0114] First, the Si substrate serves as a bulk, and accordingly, (N₀,(n₀, k₀)) of the aforementioned Si substrate can be easily determined.On the other hand, (d, N, (n, k)) of the thin film on the substrate aredetermined using the Effective Medium Approximation (EMA), andaccordingly, models for the thin film are assumed based upon severaldispersion formulae or reference data.

[0115] Now, let us say that the initial values of the model of the thinfilm are determined as follows.

[0116] Volume fraction (Vf): SiO₂(30%)+SiN_(x) (70%)

[0117] Thickness (d): 20 Å

[0118] Furthermore, multiple film thicknesses are determined within aplausible range (d±mΔd). In the same way, multiple volume fractions andmultiple incident angles are determined within a plausible ranges (Vf±mΔVf) and (φ±mΔφ), respectively.

[0119] (Fitting Step for the Parameters of the Dispersion Formula)

[0120] Fitting is made with regard to the parameters (ε_(s), ω_(t)) ofthe dispersion formula based upon the aforementioned combinations of theincident angle, the film thickness, and the volume fraction.

[0121] (Step for First Selection)

[0122] The difference between the spectrums ψ_(M)(λ_(i)) andΔ_(M)(λ_(i)) obtained by the aforementioned fitting and theaforementioned measured spectrums ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) iscalculated for each model. The fitting result (DSP_(best)) correspondingto the model with the film thickness (d_(best)), the incident angle(φ_(best)), and the volume fraction (Vf_(best)), which exhibits theminimal difference is determined.

[0123] (Step for Second Selection)

[0124] Fitting is made with regard to the film thickness (d_(best)), thevolume fraction (Vf_(best)), and the dispersion formula (DSP_(best)),with the incident angle (φ_(best)) determined in the aforementioned stepfor first selection as a fixed value. As a result, in this example, thefollowing results are obtained.

[0125] Volume fractions (Vf): SiO₂ (57.1%)+SiN_(x)(42.9%)

[0126] film thickness (d): 32.5 Å

[0127] (Step for Modification of the Model in the Event thatDetermination is Made that the Data Obtained by Fitting is Impossiblefrom the Perspective of Physics)

[0128] In some cases, the fitting results obtained in the aforementionedstep for first selection or second selection, may be unrealistic fromboth the physical and empirical perspective. In this case, determinationis made that fitting has been made using flawed models, and modificationof the models, such as change or addition of the material forming themodels, is made so as to make fitting again. The modification of themodels and the fitting using the modified model are repeated untilplausible fitting results are obtained. Note that while the step forconfirmation is necessary in practice, the aforementioned step is not anessential component in the present invention, and an arrangement may bemade wherein the step for confirmation is omitted.

[0129] (Description Regarding an Implemented Example of an AnalysisMethod for an Extremely-Thin-Film Double-Layer Structure)

[0130] Description will be made regarding an implemented example of ananalysis method according to the present invention for analyzing anextremely-thin-film double-layer structure based upon the data acquiredfrom a spectroscopic ellipsometer, with reference to the drawings andthe like.

[0131]FIG. 3 is a diagram which shows a configuration of theellipsometer used in the analysis method for an extremely-thin-filmdouble-layer structure. Note that an enlarged part of a sample 4, whichis to be measured, is shown in FIG. 3.

[0132] The processing shown in the step for acquiring the spectroscopicmeasurement data described later is performed using the spectroscopicellipsometer shown in FIG. 3. First, description will be made regardingthe measurement apparatus. A Xe lamp 1 is a so-called white light sourcefor emitting light containing a great number of wavelength components.The light emitted from the Xe lamp 1 is introduced to a polarizer 3through an optical fiber 2. The light polarized by the polarizer 3 iscast onto the surface of a sample 4 which is to be measured with apredetermined incident angle (e.g., φ=75°). Note that the sample 4 is ameasurement sample wherein two thin-film layers are formed on asubstrate described later.

[0133] The reflected light from the sample 4 is introduced to ananalyzer 6 through a photo-elastic modulator (PEM) 5. The reflectedlight is subjected to phase modulation with a frequency of 50 kHz by thephoto-elastic modulator (PEM) 5. As a result the polarization of thereflected light, which is originated from the linearly polarizedincident light, will change periodically from linearly to elliptically.Accordingly, Ψ and Δ can be determined within several msec. The outputfrom the analyzer 6 is connected to a spectroscope 8 through an opticalfiber 7. The output data from the spectroscope 8 is acquired by a dataacquisition unit 9, whereby the spectroscopic measurement step to obtainthe measured spectroscopic data ends. Note that the PEM 5 may besituated in front of the polarizer 3 or the analyzer 6.

[0134]FIG. 4 is a flowchart which shows an extremely-thin-filmdouble-layer-structure measurement method according to an embodiment ofthe present invention. FIG. 5 is an explanatory diagram for describingan analyzing stage 1B of the aforementioned embodiment in detail. FIG. 6is an explanatory diagram for describing an analyzing stage 2B of theaforementioned embodiment in detail. FIG. 7 is an explanatory diagramfor describing an analyzing stage 3B of the aforementioned embodiment indetail.

[0135] Now, reference characters are listed as follows.

[0136] (Definition of the Reference Characters)

[0137] Sub: substrate (with known optical constants, which serves as abulk)

[0138] Mat: material forming a thin film (optical constants of thematerial)

[0139] Mat_(ij): material used in the j'th model forming the i'th layer(optical constants of the i'th layer's material)

[0140] d_(i): film thickness of the i'th layer

[0141] d_(i(best)): film thickness of the i'th layer obtained by fitting

[0142] d_(ij): film thickness of the i'th layer in the j'th model

[0143] d_(ij(best)): film thickness of the i'th layer in the j'th modelobtained by fitting

[0144] χ²: mean square error (χ²)

[0145] χ² _((j)): mean square error (χ²) at the time of fitting basedupon the j'th model

[0146] Void: material with n=1, and k=0

[0147] Vf_((ij)): volume fraction of the material in the i'th layer inthe j'th model

[0148] Vf_((ij)(best)): volume fraction of the material in the i'thlayer in the j'th model obtained by fitting

[0149] (Measurement Stage: Measurement)

[0150] Measurement is made using the apparatus shown in FIG. 3. In themeasurement stage, incident light is cast onto a thin-film double-layerstructure on a substrate (see the enlarged view in FIG. 3) serving as asample 4, which is to be measured, while changing the wavelength of theincident light as a parameter, in order to obtain measured spectrumsψ_(E)(λ_(i)) and Δ_(E)(λ_(i)), which represent the change inpolarization between the incident light and the reflected light for eachwavelength λ_(i).

[0151] (Measurement Stage: Data Storage)

[0152] The data measured in the aforementioned stage is stored as thecomparative data (see FIG. 4).

[0153] (Analyzing Step 1B-1)

[0154] In this step, several models are formed based upon the (N₀, (n₀,k₀)) of the substrate, the plausible complex refractive indexes (N₁,(n₁, k₁)) and (N₂, (n₂, k₂)) of the materials (Mat 1, Mat 2) forming thethin films, and the film thicknesses (d₁, d₂).

[0155] In this implemented example, let us say that four models (1)through (4) are formed as follows. The schematic configuration of thesemodels are shown in block 31 in FIG. 5.

[0156] The model (1) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₁) and a second layer (formed of a materialhaving the optical constants of the Mat 2, with the film thickness ofd₂₁) are formed on a substrate (Sub).

[0157] The model (2) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₂) and a second layer (formed of a materialhaving the optical constants of the Mat 2, and Void, with predeterminedvolume fraction and with the film thickness of d₂₂) are formed on asubstrate (Sub). Note that the aforementioned Void represents a materialhaving the refractivity of cavities, which is 1.

[0158] The model (3) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₃) and a second layer (formed of a materialhaving the optical constants of the Mat 2, and a material having theoptical constants of the Mat 3, with the film thickness of d₂₃) areformed on a substrate (Sub). Note that the aforementioned second layer 2is formed of a mixture of the material 2 and material 3 with apredetermined volume fraction.

[0159] The model (4) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₄) and a second layer (formed of a materialhaving generally the same optical constants as the Mat 2, mixed with theVoids, with the film thickness of d₂₄) are formed on a substrate (Sub).

[0160] Here, the second layers in the aforementioned models (2) through(4) can be approximated as a uniform film using the Effective MediumApproximation (EMA), thereby obtaining optical constants of theapproximated uniform film based upon the volume fractions set to thesecond layer thereof. Note that the above-described four models areformed, making an assumption that the optical constants of the materialforming the substrate (Sub) are known, the optical constants of thefirst layer are generally known, the optical constants of the secondlayer, the film thickness d₁ of the first layer, and the film thicknessd₂ of the second layer, are unknown (uncertain).

[0161] (Analyzing Step 1B-2)

[0162] Fitting is performed with regard to each of the four models (1)through (4) formed in the above-described step 1B-1, and the measureddata ψ_(E) and Δ_(E) obtained from the above-described measuredspectrums. The mean square error values (χ²) obtained at the time offitting for the fitting parameters of each model are shown in block 32in FIG. 5.

[0163] During the fitting of the model (1), fitting is performed for thefilm thickness of d₁₁ of the first layer and the film thickness of d₂₁of the second layer, whereby the fitting results d_(11(best)) andd_(21(best)), and the mean square value χ² ₍₁₎, are obtained.

[0164] During the fitting of the model (2), fitting is performed for thefilm thickness of d₁₂ of the first layer, the film thickness of d₂₂ ofthe second layer, and the volume fraction of the second layer, wherebythe fitting results d_(12(best)), d_(22(best)), Vf_(22(best)), and themean square value χ² ₍₂₎, are obtained.

[0165] During the fitting of the model (3), fitting is performed for thefilm thickness of d₁₃ of the first layer, the film thickness of d₂₃ ofthe second layer, and the volume fraction of the second layer, wherebythe fitting results d_(13(best)), d_(23(best)), Vf_(23(best)), and themean square value χ² ₍₃₎, are obtained.

[0166] During the fitting of the model (4), fitting is performed for thefilm thickness of d₁₄ of the first layer, the film thickness of d₂₄ ofthe second layer, and the volume fraction of the second layer, wherebythe fitting results d_(14(best)), d_(24(best)), Vf_(24(best)), and themean square value χ² ₍₄₎, are obtained.

[0167] (Analyzing Step 1B-3)

[0168] In this step shown in block 33 in FIG. 5, the fitting resultscorresponding to the model which exhibits the minimal χ² value, or thefitting results, of which the film thicknesses and the volume fractionare in predetermined ranges, corresponding to the model which exhibitsthe minimal χ² value, are selected from the fitting results obtained inthe fitting for the aforementioned multiple models.

[0169] (Analyzing Step 2B-1)

[0170] A model (initial values) used in the analyzing step 2 is shown inblock 41 in FIG. 6. In this example, the optical constants of the Mat 1are generally known, and accordingly, the optical constants of the Mat 1used in the analyzing stage 1B are used without change. The opticalconstants of the material (Mat 2) forming the second layer are unknown,and accordingly, in this case, the dispersion formula is employed. Notethat the film thicknesses obtained in the analyzing step 1B-3 are usedas the initial values of the film thicknesses (d).

[0171] (Analyzing Step 2B-2)

[0172] In this step, as shown in block 42 in FIG. 6, five sub-models areformed as follows:

[0173]1) A sub-model having the same structure as shown in block 41 inFIG. 6;

[0174]2) A sub-model having a structure wherein the film thickness ofthe first layer d_(1(best)) of the structure shown in block 41 ischanged by +10%;

[0175]3) A sub-model having a structure wherein the film thickness ofthe first layer d_(1(best)) of the structure shown in block 41 ischanged by +5%;

[0176]4) A sub-model having a structure wherein the film thickness ofthe first layer d_(1(best)) of the structure shown in block 41 ischanged by −5%; and

[0177]5) A sub-model having a structure wherein the film thickness ofthe first layer d_(1(best)) of the structure shown in block 41 ischanged by −10%.

[0178] Subsequently, BLMC is performed for each of the aforementionedfive sub-models while changing the film thickness of the second layer(d_(2(best))) within a range of ±10% as a parameter. Thus, the filmthickness of the second layer d_(2j), the optical constants thereofMat_(2j), and the χ² value χ² _((j)) are obtained. Note that jrepresents the index number of each sub-model.

[0179] (Analyzing Step 2B-3)

[0180] In this step, the fitting results corresponding to the modelwhich exhibits the minimal χ² value, or the fitting results, of whichthe film thicknesses and the parameters of the dispersion formula are inpredetermined ranges, corresponding to the model which exhibits theminimal χ² value, are selected from the fitting results obtained in theaforementioned step 2B-2 (see the block 43 in FIG. 6). Note that in theevent that determination is made that the fitting results are impossiblefrom the perspective of physics, the flow returns to the analyzing stage1B, and modeling is made again, following which fitting is performedagain (step 2B-2).

[0181] (Analyzing Step 3B-1)

[0182] Fitting is performed for the film thicknesses of the first andsecond layers with the optical constants of the first layer and secondlayer being fixed to the results corresponding to the model selected inthe above-described analyzing step 2B-3. Alternately, fitting isperformed for the film thicknesses of the first and second layers, andthe optical constants of the second layer, with the optical constants ofthe first layer being fixed (see the block 51 in FIG. 7).

[0183] (Analyzing Step 3B-2)

[0184] Confirmation is made that the film thickness and the parametersof the dispersion formula, which have been obtained as the fittingresults exhibiting the minimal χ² value in the above-described step3B-1, are within predetermined ranges (see the block 52 in FIG. 7). Notethat in the event that determination is made that the obtained fittingresults are impossible from the perspective of physics, the flow returnsto the analyzing stage 1B, and modeling is made again, following whichfitting is performed again (step 2B-2).

[0185] (Analyzing Step 3B-3)

[0186] In the event that determination has been made that the obtainedfitting results are plausible from the perspective of physics in theabove-described step 3B-2, the obtained fitting results are stored (seethe block 53 in FIG. 7).

IMPLEMENTED EXAMPLE

[0187] Next, description will be made regarding an implemented examplefor analyzing a structure wherein the optical constants of the firstlayer are generally known, and the optical constants of the second layerand the film thicknesses of the first and second layer are unknown, inthe same way as with the above-described implemented example. In thiscase, description can be made with reference to the flowchart shown inFIG. 4 described above, without change. In the present implementedexample, analysis is made for a structure wherein a first layer of SiO₂and a second layer of SiN_(x) are formed on a substrate (Sub) of Si.

[0188] First, measurement is made for a sample having the aforementionedstructure using an apparatus shown in FIG. 3. That is to say, theincident light is cast onto the thin-film double-layer structure on thesubstrate serving as a sample 4, which is to be measured, in order toobtain the change in polarization between the incident light and thereflected light while changing the wavelength of the incident light as aparameter. As a result, the χ_(E) and Δ_(E) spectrums, i.e., theψ_(E)(λ_(i)) and Δ_(E)(λ_(i)), which represent the change inpolarization between the incident light and the reflected light, areobtained for each wavelength λ_(i). Subsequently, the obtained data isstored as the comparative data.

[0189] In the analyzing stage 1B shown in FIG. 5, several models areformed based upon the plausible complex refractive indexes (N₁, (n₁,k₁)) and (N₂, (n₂, k₂)) of the materials (SiO₂, SiN_(x)) forming thefilms, and the plausible film thicknesses (d₁, d₂). In the presentimplemented example, let us say that four models (1) through (4) areformed as follows.

[0190] (Analyzing Step 1B-1)

[0191] The model (1) represents a film structure wherein a first layer(formed of a material having the optical constant of SiO₂, with the filmthickness of d₁₁) and a second layer (formed of a material having theoptical constants of Si₃N₄, with the film thickness of d₂₁) are formedon a substrate (Sub:Si).

[0192] The model (2) represents a film structure wherein a first layer(formed of a material having the optical constants of SiO₂, with thefilm thickness of d₁₂) and a second layer (formed of a material havingthe optical constant of Si₃N₄, and Void, with predetermined volumefraction and the film thickness of d₂₂) are formed on a substrate(Sub:Si). Note that the aforementioned Void represents a material havingthe refractivity of cavities, which is 1.

[0193] The model (3) represents a film structure wherein a first layer(formed of a material having the optical constants of SiO₂, with thefilm thickness of d₁₃) and a second layer (formed of a material havingthe optical constant of Si₃N₄ and a material having the opticalconstants of SiN_(x), with the film thickness of d₂₃) are formed on asubstrate (Sub:Si). Note that the aforementioned second layer 2 isformed of a mixture of the Si₃N₄ and SiN_(x) with a predetermined volumefraction.

[0194] The model (4) represents a film structure wherein a first layer(formed of a material having the optical constants of SiO₂, with thefilm thickness of d₁₄) and a second layer (formed of a material havingthe optical constants of SiN_(x) (known optical constants of a samplewith a similar composition are used) and the Void, with the filmthickness of d₂₄) are formed on a substrate (Sub:Si). Here, the secondlayers in the aforementioned models (2) through (4) can be approximatedas a uniform film using the Effective Medium Approximation (EMA),thereby obtaining optical constants of the approximated uniform filmbased upon the volume fractions set to the second layer thereof.

[0195] Note that the above-described four models are formed, making anassumption that the optical constants of the material forming thesubstrate (Sub) are known, the optical constants of SiO₂ forming thefirst layer are generally known, and the optical constants of SiN_(x)forming the second layer, the film thickness d₁ of the first layer, andthe film thickness d₂ of the second layer, are unknown (uncertain).

[0196] (Analyzing Step 1B-2)

[0197] Fitting is performed with regard to each of the four models (1)through (4) formed in the above-described step 1B-1, and the measureddata ψ_(E) and Δ_(E) obtained from the above-described measuredspectrums. The mean square error values (χ²) obtained at the time offitting for the fitting parameters of each model are shown in block 32in FIG. 5.

[0198] During the fitting of the model (1), fitting is performed for thefilm thickness of d₁₁ of the first layer and the film thickness of d₂₁of the second layer, whereby the fitting results d_(11(best)) andd_(21(best)), and the mean square value χ² ₍₁₎, are obtained.

[0199] During the fitting of the model (2), fitting is performed for thefilm thickness of d₁₂ of the first layer, the film thickness of d₂₂ ofthe second layer, and the volume fraction of the second layer, wherebythe fitting results d_(12(best)), d_(22(best)), Vf_(22(best)), and themean square value χ² ₍₂₎, are obtained.

[0200] During the fitting of the model (3), fitting is performed for thefilm thickness of d₁₃ of the first layer, the film thickness of d₂₃ ofthe second layer, and the volume fraction of the second layer, wherebythe fitting results d_(13(best)), d_(23(best)), Vf_(23(best)), and themean square value χ² ₍₃₎, are obtained.

[0201] During the fitting of the model (4), fitting is performed for thefilm thickness of d₁₄ of the first layer, the film thickness of d₂₄ ofthe second layer, and the volume fraction of the second layer, wherebythe fitting results d_(14(best)), d_(24(best)), Vf_(24(best)), and themean square value χ² ₍₄₎, are obtained.

[0202] (Analyzing Step 1B-3)

[0203] In this step shown in block 33 in FIG. 5, the fitting resultscorresponding to the model which exhibits the minimal χ² value, or thefitting results, of which the film thicknesses and the volume fractionare in predetermined ranges, corresponding to the model which exhibitsthe minimal χ² value, are selected from the fitting results obtained inthe fitting for the aforementioned multiple models.

[0204] Note that the processing from analyzing step 2B-1 to analyzingstep 3B-3 is performed in the same way as described above.

[0205] (Description Regarding an Implemented Example of an AnalysisMethod for Analyzing a Thin-Film Multi-Layer Structure)

[0206] Description will be made below regarding an analysis method foranalyzing a thin-film multi-layer structure based upon spectroscopicdata acquired from a spectroscopic ellipsometer according to the presentinvention with reference to the drawings and the like.

[0207]FIG. 8 is a schematic diagram which shows a configuration of anellipsometer employed in the analysis method for analyzing a thin-filmmulti-layer structure.

[0208] In general, the present invention can be applied to an analysismethod for analyzing an extremely-thin-film multi-layer structure and athin-film multi-layer structure, having two or more layers. First,description will be made regarding an extremely-thin-film triple-layerstructure as an example, for simplification. Note that FIG. 8 shows anenlarged part of the sample 4 which is to be measured.

[0209] The processing shown in the step for acquiring the spectroscopicmeasurement data described later is performed using the spectroscopicellipsometer shown in FIG. 8. First, description will be made regardingthe measurement apparatus. A Xe lamp 1 is a so-called white light sourcefor emitting light containing a great number of wavelength components.The light emitted from the Xe lamp 1 is introduced to a polarizer 3through an optical fiber 2. The light polarized by the polarizer 3 iscast onto the surface of a sample 4 which is to be measured with apredetermined incident angle (e.g., φ=75°). Note that the sample 4 is ameasurement sample wherein three thin-film layers are formed on asubstrate described later.

[0210] The reflected light from the sample 4 is introduced to ananalyzer 6 through a photo-elastic modulator (PEM) 5. The reflectedlight is subjected to phase modulation with a frequency of 50 kHz by thephoto-elastic modulator (PEM) 5. As a result the polarization of thereflected light, which is originated from the linearly polarizedincident light, will change periodically from linearly to elliptically.Accordingly, Ψ and Δ can be determined within several msec. The outputfrom the analyzer 6 is connected to a spectroscope 8 through an opticalfiber 7. The output data from the spectroscope 8 is acquired by a dataacquisition unit 9, whereby the spectroscopic measurement step to obtainthe measured spectroscopic data ends. Note that the PEM 5 may besituated in front of the polarizer 3 or the analyzer 6.

[0211]FIG. 9 is a flowchart which shows an extremely-thin-filmtriple-layer measurement method, and FIG. 15 is a flowchart which showsan analysis method for analyzing a thin-film n-layer structure, which isa generalized arrangement according to the present invention.

[0212] Generally, the analysis method according to the present inventioncan be classified into three phases for facilitating discussion. Inanalyzing phase 1C, the initial model, which is to be analyzed in stepsfollowing analyzing phase 2C, and is assumed to match an actual sample,is determined.

[0213] In the phase 1C, as described later, an arrangement may be madewherein a single best-first-approximation model (which will be referredto as “BFAM” hereafter) is selected as the initial model from multiplemodels by fitting (see the blocks 31, 32, and 33, in FIG. 10, and theblock 81A in FIG. 15), or an arrangement may be made wherein the initialmodel is assumed or formed based upon known data (see the block 34 inFIG. 10, and the block 81B in FIG. 15). In either case, the selectedinitial model in the phase 1 is analyzed in steps from the analyzingphase 2C on.

[0214] The number of models, from which the aforementioned model (BFAM)are selected in analyzing phase 1C, is dependent upon the number ofunknown layers in a structure of a sample and the number of availabledata sets. Note that the unknown layer used here means a layer or thelike of which the precise optical constants need to be determined.

[0215] In the analyzing phase 2C, the EBLMC method is performed forunknown materials forming multi-layer structure. Specifically, the EBLMCmethod is performed for each unknown material in order of uncertaintythereof in the analyzing stage 2C-1, the analyzing stage 2C-2, and soforth.

[0216] For example, in the analyzing stage 2C-1, the EBLMC method isperformed for the Mat 2 as described later. Subsequently, in analyzingstage 2C-2, the EBLMC method is performed for the Mat 3 using theresults obtained in the analyzing stage 2C-1. In the analyzing phase 3C,final fitting is made for the results obtained in the analyzing phase2C, and the obtained data is confirmed, and output or stored.

[0217] Now, reference characters are listed as follows.

[0218] (Definition of the Reference Characters)

[0219] Sub: substrate (with known optical constants, which serves as abulk)

[0220] Mat: material forming a thin film (optical constants of thematerial)

[0221] d_(i): film thickness of the i'th layer

[0222] d_(i(best)): film thickness of the i'th layer obtained by fitting

[0223] d_(ij): film thickness of the i'th layer in the j'th model

[0224] d_(ij(best)): film thickness of the i'th layer in the j'th modelobtained by fitting

[0225] χ²: mean square error (χ²)

[0226] χ² _((j)): mean square error (χ²) at the time of fitting basedupon the j'th model

[0227] Void: material with n=1, and k=0

[0228] Vf_((ij)): volume fraction of the material in the i'th layer inthe j'th model

[0229] Vf_((ij)(best)): volume fraction of the material in the i'thlayer in the j'th model obtained by fitting

[0230] Now, description will be made regarding an implemented examplefor analyzing a sample having a structure as follows. The third layer:TaO_(x) (Mat₃): d₃ The second layer: SiN (Mat₂): d₂ The first layer:SiO₂ (Mat₁): d₁ Substrate (Sub): Si: bulk

[0231] Measurement shown in block 20-1 (measurement step in thespectroscopic measurement phase) in FIG. 9 is performed using anapparatus shown in FIG. 8. The incident light is cast onto anextremely-thin-film triple-layer structure on the substrate (see theenlarged view in the drawing) serving as a sample 4 in order to obtainthe change in polarization between the incident light and the reflectedlight while changing the wavelength of the incident light as aparameter. As a result, the ψ_(E) and Δ_(E) spectrums, i.e., theψ_(E)(λ_(i)) and Δ_(E)(λ_(i)), which represent the change inpolarization between the incident light and the reflected light, areobtained for each wavelength λ_(i). In the data storage block 20-2 inthe spectroscopic measurement phase, the data obtained in the previousstep is stored as the comparative data (see FIG. 9).

[0232] (Extremely-Thin-Film Triple-Layer-Structure Fitting Process)

[0233] Next, description will be made regarding an implemented examplefor analyzing a structure wherein the optical constants of the material1 (Mat 1) forming the first layer are generally known, and the opticalconstants of the materials 2 and 3 forming the second and third layersand the film thicknesses (d₁, d₂, and d₃) of the first, second, andthird layers are unknown. Note that, in this example, let us say thatthe optical constants of the second layer are the least known.

[0234] In the analyzing phase 1C, the processing described in blocks 31through 33 shown in FIG. 10 are performed, whereby the BFAM isdetermined as an initial model. Alternately, the initial model isassumed as shown in block 34 in FIG. 10.

[0235] (Analyzing Step 1C-1)

[0236] As shown in block 31 in FIG. 10, multiple kinds of plausiblemodels are formed. Subsequently, the model having the structure and thefilm thicknesses which match the measured results best in the initialstage is determined.

[0237] In this step, several models are formed based upon the (N₀, (n₀,k₀)) of the substrate, and the plausible complex refractive indexes (N₁,(n₁, k₁)), (N₂, (n₂, k₂)), and (N₃, (n₃, k₃)) of the materials (Mat 1,Mat 2, Mat 3) forming the thin films, and the film thicknesses (d₁, d₂,d₃).

[0238] In the present implemented example, let us say that four models(1) through (4) are formed as follows. Note that the schematicstructures of the aforementioned models are shown in block 31 in FIG.10.

[0239] The model (1) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₁), a second layer (formed of a material havingthe optical constants of the Mat 2 with the film thickness of d₂₁), anda third layer (formed of a material having the optical constants of theMat 3 with the film thickness of d₃₁), are formed on a substrate (Sub).

[0240] The model (2) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₂), a second layer (formed of a material havingthe optical constants of the Mat 2, and the Void, with the filmthickness of d₂₂), and a third layer (formed of a material having theoptical constants of the Mat 3, and the Void, with the film thickness ofd₃₂), are formed on a substrate (Sub). Note that the aforementioned Voidrepresents a material having the refractivity of cavities, which is 1.

[0241] The model (3) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₃), a second layer (formed of a material havingthe optical constants obtained by measuring a material similar to theMat 2, and the Void, with the film thickness of d₂₃), and a third layer(formed of a material having the optical constants obtained by measuringa material similar to the Mat 3, and the Void, with the film thicknessof d₃₃), are formed on a substrate (Sub).

[0242] The model (4) represents a film structure wherein a first layer(formed of a material having the optical constants of the Mat 1, withthe film thickness of d₁₄), a second layer (formed of a material havingthe optical constants of the Mat 2, and a material having the opticalconstants of the Mat 2′, with the film thickness of d₂₄), and a thirdlayer (formed of a material having the optical constants of the Mat 3,and a material having the optical constants of the Mat 3′, with the filmthickness of d₃₄), are formed on a substrate (Sub).

[0243] Here, each of the second layer and the third layer in theaforementioned models (2) through (4) can be approximated as uniformfilms using the Effective Medium Approximation (EMA), thereby obtainingoptical constants of the approximated uniform films based upon thevolume fraction set to the second layer and the third layer thereof.Note that the above-described four models are formed, making anassumption that the optical constants of the material forming thesubstrate (Sub) are known, the optical constants of the first layer aregenerally known, and the optical constants of the second layer and thethird layer, the film thickness d₁ of the first layer, the filmthickness d₂ of the second layer, and the film thickness d₃ of the thirdlayer, are unknown (uncertain).

[0244] (Analyzing Step 1C-2)

[0245] Fitting is performed with regard to each of the four models (1)through (4) formed in the above-described analyzing step 1C-1, and themeasured data ψ_(E) and Δ_(E) obtained from the above-described measuredspectrums. The mean square error values (χ²) obtained at the time offitting for the fitting parameters of each model are shown in block 32in FIG. 10.

[0246] During the fitting of the model (1), fitting is performed for thefilm thickness of d₁₁ of the first layer, the film thickness of d₂₁ ofthe second layer, the film thickness of d₃₁ of the third layer, and theincident angle φ₁, whereby the fitting results d_(11(best)),d_(21(best)), d_(31(best)), φ_(1(best)), and the mean square value (χ²value) χ² ₍₁₎, are obtained.

[0247] During the fitting of the model (2), fitting is performed for thefilm thickness of d₁₂ of the first layer, the film thickness of d₂₂ ofthe second layer, the film thickness of d₃₂ of the third layer, thevolume fraction Vf₂₂ of the second layer, the volume fraction Vf₃₂ ofthe third layer, and the incident angle φ₂, whereby the fitting resultsd_(12(best)), d_(22(best)), d_(32(best)), Vf_(22(best)), Vf_(32(best)),φ_(2(best)), and the mean square value (χ² value) χ² ₍₂₎, are obtained.

[0248] During the fitting of the model (3), fitting is performed for thefilm thickness of d₁₃ of the first layer, the film thickness of d₂₃ ofthe second layer, the film thickness of d₃₃ of the third layer, thevolume fraction Vf₂₃ of the second layer, the volume fraction Vf₃₃ ofthe third layer, and the incident φ₃, whereby the fitting resultsd_(13(best)), d_(23(best)), d_(33(best)), Vf_(23(best)), Vf_(33(best)),φ_(3(best)), and the mean square value (χ² value) φ² ₍₃₎, are obtained.

[0249] During the fitting of the model (4), fitting is performed for thefilm thickness of d₁₄ of the first layer, the film thickness of d₂₄ ofthe second layer, the film thickness of d₃₄ of the third layer, thevolume fraction Vf₂₄ of the second layer, the volume fraction Vf₃₄ ofthe third layer, and the incident angle φ₄, whereby the fitting resultsd_(14(best)), d_(24(best)), d_(34(best)), Vf_(24(best)), Vf_(34(best)),φ_(4(best)), and the mean square value (χ² value) χ² ₍₄₎, are obtained.

[0250] (Analyzing Step 1C-3)

[0251] In this step, the fitting results corresponding to the modelwhich exhibits the minimal χ² value, or the fitting results, of whichthe film thicknesses, the volume fractions, and the incident angle, arein predetermined ranges, corresponding to the model which exhibits theminimal χ² value, are selected from the fitting results obtained in thefitting for the aforementioned multiple models, as shown in block 33 inFIG. 10.

[0252] In the analyzing phase 2C, EBLMC is performed in order ofuncertainty of the material.

[0253] The BFAM, which serves as a model employed in the analyzing phase2C, is shown in block 41 in FIG. 11.

[0254] In this example, let us say that the fitting results based uponthe model (4) in the analyzing phase 1C exhibits the minimal χ² value.Here, the optical constants of the second layer are replaced by a singledispersion formula. In this case, all the film thicknesses (d₁, d₂, d₃),the optical constants of the first and third layers, and the volumefraction of the third layer, are determined based upon the fittingresults obtained in the above-described analyzing phase 1C.

[0255] (Analyzing Step 2C-1-2)

[0256] In this example, as shown in FIG. 11, BLMC is performed for thesecond layer with the film thickness of the first layer fixed to thevalue described below, while changing both the film thickness of thethird layer and the volume fraction thereof around ±10% as parameters.In a step shown in block 42-1, BLMC is performed for the Mat 2 (DSP) ofthe second layer with the film thickness d₁ of the first layer fixed tothe d_(1(best))−10%, while changing the film thickness d₃ within aroundd_(3(best))±10%, and the volume fraction Vf₁ within aroundVf_(1(best))±10%. The above-described step shown in block 42-1 (in acase wherein d₁ is fixed to the d_(1(best))−10%) is shown in detail inFIG. 14.

[0257] First, description will be made regarding a step shown in block42-1-2-f as an example. In this case, BLMC is performed for the secondlayer with the Vf₁ fixed to Vf_(1(best)) while changing the filmthickness d₃ within±10% around d_(3(best)), whereby fitting results,i.e., the film thicknesses, the optical constants thereof, and the χ²value, are obtained for each film thickness d₃ as a parameter. Thefitting results which exhibits the minimal χ² value is selected as thefitting results in the step shown in block 42-1-2-s. The same processingas in block 42-1-2-f is performed in the steps shown in blocks 42-1-1-f,42-1-3-f, and so forth, with the Vf₁ being fixed to a predeterminedvalue within ±10% around Vf_(1(best)). In each case, the best fittingresults which exhibit the minimal χ² value are selected in blocks42-1-1-s, 42-1-3-s, and so forth, as well. Furthermore, the best fittingresults which exhibit the minimal χ² value are selected from theaforementioned fitting results obtained based upon the models with theVf₁ as a parameter (see FIG. 11 and block 42-1-1 in FIG. 14).

[0258] Furthermore, in step shown in block 42-2 in FIG. 11, BLMC isperformed with the d₁ fixed to the d_(1(best)), in the same way as shownin block 42-1 described above. Furthermore, in step shown in block 42-3in FIG. 11, BLMC is performed with the d₁ fixed to the d_(1(best))±10%,in the same way as shown in block 42-1 described above. In each case,the best fitting results which exhibit the minimal χ² value are selectedin blocks 42-2-1, 42-3-1, and so forth, in the same way as in theaforementioned block 42-1-1. Furthermore, the best fitting results whichexhibit the minimal χ² value are selected from the aforementionedfitting results obtained based upon the models with the d₁ as aparameter (see block 43 in FIG. 11).

[0259] (Analyzing Phase 2C-2-1)

[0260] In the analyzing phase 2C-2-1, the optical constants of the thirdlayer are replaced by a single dispersion formula as shown in FIG. 12(see step 1 shown in block 51 in FIG. 12). All the film thicknesses (d₁,d₂, d₃), and the optical constants of the first and second layers, aredetermined based upon the fitting results in the analyzing stage 2C-1.

[0261] (Analyzing Step 2C-2-2)

[0262] EBLMC is performed for the model determined in the aforementionedstep 2C-2-1. Specifically, BLMC is performed for the third layer whilechanging the film thickness d₁ of the first layer as a parameter in arange of ±10% around d_(1(best)), as well as changing the film thicknessd₂ of the second layer as a parameter in the range of ±10% aroundd_(2(best)).

[0263] (Analyzing Step 2C-2-3)

[0264] In the step shown in block 53 in FIG. 12, the best fittingresults which exhibit the minimal χ² value are selected from theaforementioned fitting results obtained in the above-described analyzingstep 2C-2-2. Note that in the event that determined kinds of the fittingresults, i.e., film thicknesses, the parameters of the dispersionformula, the volume fractions, and the incident angle, deviate frompredetermined ranges, the flow returns to the analyzing stage 2C-1. Notethat in the event that determined kinds of the fitting results arewithin the predetermined ranges, the flow proceeds next processing.

[0265] (Analyzing Step 3C-1)

[0266]FIG. 13 shows analyzing phase 3C serving as the final analyzingphase. In analyzing step 3C-1 shown in FIG. 13, fitting is made for themodel, which exhibits the best χ² value in the above-described analyzingstep 2C-2-3, as follows.

[0267] Fitting is made for all the film thicknesses with all the opticalconstants thereof being fixed. Alternately, fitting is made for all thefilm thicknesses and the optical constants of the second layer with theoptical constants of the first and third layers being fixed.Alternately, fitting is made for all the film thicknesses and theoptical constants of the third layer with the optical constants of thefirst and second layers being fixed. Alternately, fitting is made forall the film thicknesses and the optical constants of the second andthird layers with the optical constants of the first layer being fixed.

[0268] (Analyzing Step 3C-2)

[0269] In analyzing step 3C-2 shown in block 62 in FIG. 13, confirmationis made for fitting results obtained in the above-described analyzingstep 3C-1. For example, confirmation is made whether or not the obtainedfitting results are within predetermined ranges. In the event thatdetermination is made that the obtained fitting results deviate from thepredetermined ranges, the flow returns to the above-described analyzingphase 1C.

[0270] (Analyzing Step 3C-3)

[0271] In analyzing step 3C-3 shown in block 63 in FIG. 13, the fittingresults which have passed the aforementioned confirmation described inanalyzing step 3C-2 are stored.

[0272] According to the present invention:

[0273] 1. Reliable film thicknesses (of all the layers) and opticalconstants (of at least two layers in a film structure) can be obtained,even for a multi-layer structure (in particular, Ultra-thin-filmmulti-layer structure) in spite of the strong correlation there between.

[0274] 2. In BFAM determination step, the number of required plausibleunknown variables can be suppressed to a minimum.

[0275] 3. EBLMC is performed in an appropriate order, therebydrastically reducing the possibility to obtain wrong local minimum, andthereby improving the reliability of the fitting results.

[0276] 4. With the method according to the present invention, the filmthicknesses and the optical constants of a multi-layer structure can bedetermined, even in a case wherein the multi-layer structure contains alarge number of unknown materials.

[0277] Various modifications can be made within the scope of the presentinvention. To facilitate understanding, description has been maderegarding acquisition of data and setting of models, using Ψ and Δ,throughout the present specification. Furthermore, the measurement andfitting can be performed in the same way for data set of (n, k), (ε_(i),ε_(r)), (tan Ψ, cos Δ), or (I_(s), I_(c)), well known by one skilled inthe art, and are encompassed in the present invention.

[0278] While description has been made regarding an implemented examplefor analyzing a single-layer structure wherein a SiO_(x) or SION layerare formed on a substrate, an implemented example for analyzing adouble-layer structure wherein SiO₂ and SiN_(x) layers are formed on asubstrate, or an implemented example for analyzing a triple-layerstructure wherein SiO₂, SiN_(x), and TaO_(x) layers are formed on asubstrate, the present invention may be applied to a single-layerstructure or multi-layer structure formed of a wide variety of materialsin a wide range of film thickness in the same way.

[0279] While description has been made regarding an arrangement whereinknown values (reference data) are employed for the optical constants, anarrangement may be made wherein the optical constants are calculatedbased upon the dispersion formula or the like which represents thewavelength dependency of the dielectric constant of the material, whichis encompassed in the technical scope of the present invention.Furthermore, in a case of using a dispersion formula, an arrangement maybe made wherein known values are employed for optical constants, whichis encompassed in the technical scope of the present invention.

[0280] While description has been made regarding an arrangement whereinmeasurement is made using an ellipsometer with the PEM, an arrangementmay be made wherein measurement is made using an ellipsometer withoutthe PEM.

[0281] The present invention can be similarly applied to an arrangementwherein a substrate other than Si substrate, such as a transparentsubstrate formed of glass, quartz, or the like, a compound semiconductorsubstrate, or the like, is employed. Furthermore, the present inventionis not restricted to any particular kind of substrate, but rather thepresent invention can be applied to a substrate with any surface state,i.e., the present invention can be applied to both smooth and roughsubstrates.

[0282] The dispersion formulas used for the present invention includenot only the formula based upon classical mechanics or quantum mechanicsand empirical formulas, but also various other formulas including otherparameters, which are encompassed in the technical scope of the presentinvention.

[0283] While description has been made regarding an arrangement whereinmeasurement is made using the EMA, an arrangement may be made whereinother effective medium theory is employed, which is also encompassed inthe technical scope of the present invention.

[0284] Part or all of the above described methods can be performedautomatically (by a computer, robot, or the like) or manually, which isalso encompassed in the technical scope of the present invention.

[0285] Description has been made regarding an arrangement whereinmeasurement is made with an incident angle of 75°, but an arrangementmay be made wherein measurement is made with an incident angle otherthan the aforementioned angle, which is also included in the technicalscope of the present invention.

[0286] While description has been made regarding a method for analyzingby taking an incident angle around the nominal incident angle (75°) as aparameter, an arrangement may be made wherein analysis is made taking anincident angle around the measured incident angle as a parameter, whichis also encompassed in the technical scope of the present invention.

[0287] Furthermore, an arrangement may be made wherein measurement ismade with multiple incident angles automatically (Variable AngleMeasurement), and analysis is made based upon all of the measured data,or based upon the data with regard to a specified angle of theaforementioned multiple incident angles, which is also encompassed inthe technical scope of the present invention. Furthermore, anarrangement may be made wherein fitting is performed for all of themeasured data, or for the data with regard to the specified incidentangle, taking an incident angle around each measuring incident angle asa parameter, which is encompassed in the technical scope of the presentinvention.

[0288] While description has been made regarding an implemented examplefor analyzing a single-layer structure, a double-layer structure, or atriple-layer structure, formed of extremely-thin-films (Mat 1, Mat 2,Mat 3) on a substrate, the present invention is not restricted to anarrangement for analyzing a structure formed of extremely-thin-filmdielectric materials, rather, the present invention may be applied to anarrangement for analyzing a structure formed of a wide variety ofmaterials in a wide range of film thickness in the same way.

[0289] Furthermore, an arrangement may be made wherein all or a part ofthe above-described method are performed, which is also encompassed inthe technical scope of the present invention.

[0290] While description has been made regarding an implemented examplefor performing fitting with regard to desired parameters at the sametime, an arrangement may be made wherein the parameters are divided intomultiple groups so as to perform fitting for each parameter group, whichis also encompassed in the technical scope of the present invention.

[0291] In some cases, fitting is made for the incident angle with BLMCforming a part of EBLMC, as described above. In this case, descriptionhas been made regarding an implemented example for performing fittingwith regard to the incident angle and a wide variety of parameters atthe same time, an arrangement may be made wherein separate fitting ismade for the incident angle and the other parameters, or an arrangementmay be made wherein fitting is made for the parameters of the filmstructure with the incident angle being fixed, which are alsoencompassed in the technical scope of the present invention.

[0292] Furthermore, an arrangement may be made wherein fitting is madefor the incident angle using fitting methods other than BLMC, which isalso encompassed in the technical scope of the present invention.

[0293] While description has been made regarding an implemented examplefor performing BLMC or EBLMC for multiple models with a predeterminedparameter being fixed at and around the median thereof in a range of±10% in increments of 5%, an arrangement may be made for performing BLMCor EBLMC for multiple models with a predetermined parameter being fixedat and around the median thereof in other ranges and in otherincrements. Furthermore, while description has been made regarding animplemented example wherein the range and the increments of theaforementioned parameter have been expressed in terms of percent (%), anarrangement may be made wherein the range and the increments of theaforementioned parameter are expressed in terms of the minimal value,the maximal value, and the number of increment steps, which is alsoencompassed in the technical scope of the present invention.

[0294] While description has been made regarding an implemented examplewherein EBLMC is performed for materials in order of uncertaintythereof, which is an effective method, an arrangement may be madewherein EBLMC is performed in other orders, which is also encompassed inthe technical scope of the present invention.

[0295] While description has been made regarding an implemented examplewherein the obtained data is stored in a step forming the measurementand analyzing step, an arrangement may be made wherein the obtained datais stored even following completion of the analysis process (i.e., theobtained data can be used following completion of the analysis process),or an arrangement may be made wherein the obtained data is temporarilystored during the analysis process, which are also encompassed in thetechnical scope of the present invention.

[0296] While description has been made regarding an implemented examplewherein one through four models are formed based upon a mixture of SiO₂,SiN_(x), Si₃N₄, and Void, in the model-preparation step, an arrangementmay be made wherein these models are formed based upon a mixture of awide variety of materials, which is also encompassed in the technicalscope of the present invention. Note that the kind and the number of themodel varies corresponding to the conditions at the time ofmanufacturing process, unknown data, or the like.

[0297] While description has been made regarding an implemented examplewherein fitting is made for a combination of the incident angle and thefilm thicknesses, in some case, an arrangement may be made whereinfitting is made for the incident angle and the parameters of thedispersion formula at the same time, which is also encompassed in thetechnical scope of the present invention.

[0298] While description has been made regarding an implemented examplewherein fitting is made using the mean square error, an arrangement maybe made wherein fitting is made using parameters other than the χ²value, which is also encompassed in the technical scope of the presentinvention.

[0299] While description has been made regarding an implemented examplefor analyzing a layer formed of a mixture of two materials, anarrangement may be made for analyzing a layer formed of a mixture ofthree or more materials, which is also encompassed in the technicalscope of the present invention.

1. An extremely-thin-film measurement and thin-film measurement methodfor analyzing spectroscopic data acquired from a spectroscopicellipsometer using best-local-minimum-calculation (BLMC), said methodcomprising: a spectrum measurement step wherein incident light is castonto a thin film on a substrate which is to be measured while changingthe wavelength of the incident light as a parameter in order to obtainthe ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i))for each wavelength λ_(i), which represent the change in polarizationbetween the incident light and the reflected light; a step for assumingthe complex refractive index (N₀, (n₀, k₀)) of said substrate, thecomplex refractive index (N, (n, k)) of said film, based upon thedispersion formula, a plurality of film thicknesses (d±mΔd) within aplausible range, and a plurality of incident angles (φ±mΔφ) within aplausible range; a step for performing fitting for the parameters of thedispersion formula (DSP) based upon combinations of said incident angleand said film thickness; an analyzing step 1A for selecting fittingresults (DSP_(best)) obtained based upon a model formed of a combinationof said film thickness (d_(best)) and said incident angle φ_(best)),which exhibits the minimal difference between the ψ_(M)(λ_(i)) andΔ_(M)(λ_(i)) obtained by said fitting and said measured ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)); and an analyzing step 2A for performing fitting for thefilm thickness (d_(best)) and the dispersion formula (DSP_(best)) withthe incident angle (φ_(best)) obtained in said analyzing step 1A beingfixed.
 2. An extremely-thin-film measurement And thin-film measurementmethod for analyzing spectroscopic data acquired from a spectroscopicellipsometer using best-local-minimum-calculation (BLMC) according toclaim 1, wherein in said analyzing step 1A and analyzing step 2A, themean square error (χ²) is calculated from the measured values and thefitting results for each model, and the fitting results which exhibitthe minimal mean square error (χ²) are selected.
 3. Anextremely-thin-film measurement and thin-film measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometerusing best-local-minimum-calculation (BLMC), said method comprising: aspectrum measurement step wherein incident light is cast onto a thinfilm on a substrate which is to be measured while changing thewavelength of the incident light as a parameter in order to obtain theψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) foreach wavelength λ_(i), which represent the change in polarizationbetween the incident light and the reflected light; a step for formingmodels of said film structure, wherein a thin film on a substrate isformed with microscopic non-uniformity, or is formed of a mixture ofseveral materials, with the complex refractive index (N₀, (n₀, k₀)) ofsaid substrate and the complex refractive index (N, (n, k)) of saidfilm, assumed based upon several dispersion formulas or reference data,which are used for Effective Medium Approximation (EMA); a step forassuming a plurality of film thicknesses (d±mΔd) within a plausiblerange, a plurality of volume fractions (Vf±mΔVf) within a plausiblerange obtained based upon said dispersion formulas which have beenemployed in forming said models, and a plurality of incident angles(φ±mΔφ) within a plausible range; a step for performing fitting for theparameters of the dispersion formula (DSP) based upon combinations ofsaid incident angle, said film thickness, and said volume fraction; ananalyzing step 1A for selecting fitting results (DSP_(best)) obtainedbased upon a model formed of a combination of said film thickness(d_(best)), said incident angle (φ_(best)), and said volume fraction(Vf_(best)), which exhibits the minimal difference between theψ_(M)(λ_(i)) and Δ_(M)(λ_(i)) obtained by said fitting and said measuredψ_(E)(λ_(i)) and Δ_(E)(λ_(i)); and an analyzing step 2A for performingfitting for the film thickness (d_(best)), the volume fraction(Vf_(best)), and said dispersion formula (DSP_(best)) with the incidentangle (φ_(best)) obtained in said analyzing step 1A being fixed.
 4. Anextremely-thin-film measurement and thin-film measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometerusing best-local-minimum-calculation (BLMC), said method comprising: aspectrum measurement step wherein incident light is cast onto a thinfilm on a substrate which is to be measured while changing thewavelength of the incident light as a parameter in order to obtain theψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) foreach wavelength λ_(i), which represent the change in polarizationbetween the incident light and the reflected light; a step for assuminga plurality of measurement conditions (Z_(j)) in a plausible range andperforming processing from said second step of claim 1 or claim 3 forforming models of a film structure, to said second step, for each(Z_(j)); and an analyzing step 3A for selecting fitting results, ofwhich said parameters of said dispersion formula and said volumefraction are within predetermined ranges, exhibiting the minimal meansquare error (χ²), from the fitting results obtained based upon saidplurality of measurement conditions (Z_(i)).
 5. An extremely-thin-filmdouble-layer-structure measurement method for analyzing spectroscopicdata acquired from a spectroscopic ellipsometer, said method comprising:a spectrum measurement stage wherein incident light is cast onto anextremely-thin-film double-layer structure on a substrate which is to bemeasured while changing the wavelength of the incident light as aparameter in order to obtain the ψ_(E) and Δ_(E) spectrums, i.e., theψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) for each wavelength λ_(i), which representthe change in polarization between the incident light and the reflectedlight; an analyzing stage 1B which includes: an analyzing step 1B-1 forforming several models of said extremely-thin-film double-layerstructure on said substrate based upon the complex refractive index (N₀,(n₀, k₀)) of said substrate, the complex refractive indexes (N₁, (n₁,k₁)) and (N₂, (n₂, k₂)) of materials (Mat 1, Mat 2) of said thin filmsin plausible ranges, and the film thicknesses (d₁, d₂) in plausibleranges; an analyzing step 1B-2 for performing fitting for said measuredspectrums for each model; and an analyzing step 1B-3 for selectingfitting results (d_(1(best)), d_(2(best))) obtained based upon a modelwhich exhibits the minimal mean square error (χ²), or a model with saidfilm thicknesses being within predetermined ranges, which exhibits theminimal mean square error (χ²), from the fitting results obtained basedupon said several models; an analyzing stage 2B which includes: ananalyzing step 2B-1 for setting initial values of a new model to thefitting results obtained in said analyzing stage 1B; an analyzing step2B-2 for performing fitting for multiple models with a film-thicknesscombination as a parameter around and at the film-thickness combination(d_(1(best)), d_(2(best))) serving as the median, using BLMC; and ananalyzing step 2B-3 for selecting a model which exhibits the minimalmean square error (χ²), or a model with said film thicknesses, theparameters of the dispersion formula, and the incident angle, beingwithin predetermined ranges, which exhibits the minimal mean squareerror (χ²); an analyzing stage 3B which includes: an analyzing step 3B-1for performing the final fitting based upon the fitting results obtainedin said analyzing stage 2B; an analyzing step 3B-2 for confirming saidfitting results obtained in said analyzing step 3B-1; and an analyzingstep 3B-3 for storing said obtained fitting results.
 6. Anextremely-thin-film double-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometeraccording to claim 5, wherein in said analyzing step 2B-2, fitting isperformed using BLMC for materials formed of said double-layer structurein order of uncertainty of the optical constants thereof.
 7. Anextremely-thin-film double-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometeraccording to claims 5 or 6, further comprising: a step for formingmultiple models with the film thickness obtained in said analyzing step1B-3, of which the optical constants are more reliable than the other,as a parameter around and at the film thickness obtained in a range of afew percents to a few ten percents; a step for performing BLMC describedin said analyzing steps 2B-2 and 2B-3 for the other layer for eachmodel.
 8. An extremely-thin-film double-layer-structure measurementmethod for analyzing spectroscopic data acquired from a spectroscopicellipsometer, said method comprising: a spectrum measurement stagewherein incident light is cast onto an extremely-thin-filmdouble-layer-structure on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; ananalyzing stage 1B which includes: an analyzing step 1B-1 for formingseveral models of one of the first and second layers, which is formedwith non-uniformity or non-continuity, or is formed of a mixture ofseveral materials, with the complex refractive index (N₀, (n₀, k₀)) ofsaid substrate thereof, the complex refractive indexes (N₁, (n₁, k₁))and (N₂, (n₂, k₂)) of the materials (Mat 1, Mat 2) forming said thinfilms in plausible ranges, the volume fractions (Vf₁, Vf₂) in plausibleranges, and the film thicknesses (d₁, d₂) in plausible ranges, usingEffective Medium Approximation (EMA); an analyzing step 1B-2 forperforming fitting for said measured spectrums for each model; and ananalyzing step 1B-3 for selecting fitting results (d_(1(best)),d_(2(best)), Vf_((best))) obtained based upon a model which exhibits theminimal mean square error (χ²), or a model with said film thicknessesand said volume fractions being within predetermined ranges, whichexhibits the minimal mean square error (χ²), from the fitting resultsobtained based upon said several models; an analyzing stage 2B whichincludes: an analyzing step 2B-1 for forming new models with the initialvalues based upon the fitting results obtained in said analyzing stage1B, with the film thickness, wherein the corresponding parameters of thedispersion formula are less known than the other, as a parameter aroundthe value obtained said analyzing step 1B-3 in a range of (d₁±mΔd₁) or(d₂±mΔd₂), with the film thickness of the other layer as a parameteraround the value obtained said analyzing step 1B-3 in a range of(d₂±mΔd₂) or (d₁±mΔd₁), and with the volume fraction as a parameteraround the value obtained said analyzing step 1B-3 in a range of(Vf±mΔVf); an analyzing step 2B-2 for performing BLMC for the parametersof said layer, wherein the parameters of the dispersion formula are lessknown than the other, of said models obtained in said analyzing step2B-1; and an analyzing step 2B-3 for selecting a model which exhibitsthe minimal mean square error (χ²), or a model with the filmthicknesses, the parameters of the dispersion formula, and the incidentangle, being within predetermined ranges, which exhibits the minimalmean square error (χ²), from the fitting results obtained in saidanalyzing step 2B-2; an analyzing stage 3B which includes: an analyzingstep 3B-1 for performing fitting for said film thicknesses of both thinfilms, said volume fraction, and said parameters of the dispersionformula, or performing fitting for said film thicknesses of both thinfilms and said volume fraction, based upon the fitting results obtainedin said analyzing stage 2B; an analyzing step 3B-2 for confirming saidfitting results obtained in said analyzing step 3B-1; and an analyzingstep 3B-3 for storing said obtained fitting results.
 9. Anextremely-thin-film double-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometeraccording to claim 5 or claim 8, further comprising: a spectrummeasurement stage wherein incident light is cast onto anextremely-thin-film double-layer-structure on a substrate which is to bemeasured while changing the wavelength of the incident light as aparameter in order to obtain the ψ_(E) and Δ_(E) spectrums, i.e., theψ_(E)(λ_(i)) and Δ_(EP)(λ_(i)) for each wavelength λ_(i), whichrepresent the change in polarization between the incident light and thereflected light; a step for assuming a plurality of measurementconditions (Zi) in a plausible range, and performing processing of saidanalyzing stage 1B or analyzing step 2B-1 through 2B-3 of claim 5 orclaim 8 for each assumed measurement condition (Zi); and an analyzingstep 1B-4 or 2B-4 for selecting fitting results, which exhibit theminimal mean square error (χ²), or the parameters of the dispersionformula, and the volume fraction, are within a predetermined range, andwhich exhibit the minimal mean square error (χ²) which are selected fromthe fitting results obtained in said analyzing step.
 10. Anextremely-thin-film double-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometeraccording to any one of claims 5, 6 and 8, wherein in each of said stepsfor selecting the results which exhibit the least difference, describedin said analyzing stage 1B, 2B, and 3B, the mean square error (χ²) areobtained between the fitting results and the measured values, and thefitting results which exhibit the minimal mean square error (χ²), or thefitting results, of which the film thicknesses, the parameters of thedispersion formula, the volume fraction, and the change in the incidentangle, are within predetermined ranges, and which exhibit the minimalmean square error (χ²), are selected.
 11. A thin-filmtriple-layer-structure measurement method for analyzing spectroscopicdata acquired from a spectroscopic ellipsometer, said method comprising:a spectroscopic measurement phase for obtaining measured data using aspectroscopic ellipsometer; an analyzing phase 1C for forming an initialmodel of a thin-film triple-layer-structure; an analyzing phase 2C whichincludes: an analyzing stage 2C-1 for determining unknown parameters ofthe layer of interest forming said thin-film triple-layer-structure,using EBLMC; and an analyzing stage 2C-2 for determining parameters ofthe other layers with said parameters determined in said analyzing stage2C-1 being fixed, using EBLMC.
 12. A thin-film triple-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer, said method comprising: a spectroscopicmeasurement phase for obtaining measured data using a spectroscopicellipsometer; an analyzing phase 1C for forming an initial model of athin-film triple-layer-structure; an analyzing phase 2C which includes:an analyzing stage 2C-1 for determining unknown parameters of the layerof interest forming said thin-film triple-layer-structure, using EBLMC;and an analyzing stage 2C-2 for determining parameters of the otherlayers with said parameters determined in said analyzing stage 2C-1being fixed, using EBLMC; an analyzing phase 3C which includes: ananalyzing stage 3C-1 for performing the final fitting for the modelobtained in said analyzing phase 2C; an analyzing stage 3C-2 forconfirming the fitting results obtained in said analyzing stage 3C-1;and an analyzing stage 3C-3 for storing the fitting results obtained insaid analyzing stage 3C-2.
 13. A thin-film n-layer-structure measurementmethod for analyzing spectroscopic data acquired from a spectroscopicellipsometer, said method comprising: a spectroscopic measurement phasefor obtaining measured data using a spectroscopic ellipsometer; ananalyzing phase 1C for forming an initial model of a thin-filmn-layer-structure; and an analyzing phase 2C for determining unknownparameters of the layer of interest forming the n-layer structure basedupon said initial model which represents said thin-filmn-layer-structure, using EBLMC.
 14. A thin-film n-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer, said method comprising: a spectroscopicmeasurement phase for obtaining measured data using a spectroscopicellipsometer; an analyzing phase 1C for forming an initial model of athin-film n-layer-structure; an analyzing phase 2C for determiningunknown parameters of the layer of interest forming the n-layerstructure based upon said initial model, using EBLMC; an analyzing phase3C which includes: an analyzing stage 3C-1 for performing the finalfitting for the model obtained in said analyzing phase 2C; an analyzingstage 3C-2 for confirming the fitting results obtained in said analyzingstage 3C-1; and an analyzing stage 3C-3 for storing the fitting resultsobtained in said analyzing stage 3C-2.
 15. A thin-filmtriple-layer-structure measurement or thin-film multi-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer according to any one of claims 11 through 14,wherein analysis is made with unknown parameters as the filmthicknesses, the optical constants of unknown materials or the volumefractions.
 16. A thin-film triple-layer-structure measurement orthin-film multi-layer-structure measurement method for analyzingspectroscopic data acquired from a spectroscopic ellipsometer accordingto any one of claims 11 through 14, wherein said spectroscopicmeasurement phase includes: a spectrum measurement step wherein incidentlight is cast onto a thin-film triple-layer structure or a thin-filmmulti-layer structure on a substrate which is to be measured whilechanging the wavelength of the incident light as a parameter in order toobtain the ψ_(E) and Δ_(E) spectrums, i.e., the ψ_(E)(λ_(i)) andΔ_(E)(λ_(i)) for each wavelength λ_(i), which represent the change inpolarization between the incident light and the reflected light; and astorage step for storing the data obtained in said measured step.
 17. Athin-film triple-layer-structure measurement or thin-filmmulti-layer-structure measurement method for analyzing spectroscopicdata acquired from a spectroscopic ellipsometer according to any one ofclaims 11 through 14, wherein in said analyzing phase 1C, the singleBest First Approximation Model (which will be referred to as “BFAM”hereafter) is selected from a plurality of models by fitting, or a modelis assumed based upon known data, as said initial model, and wherein ina case of employing said BFAM, said analyzing phase 1C includes: ananalyzing step 1C-1 for forming a plurality of models within a plausiblerange; an analyzing step 1C-2 for performing fitting with regard to thefilm thicknesses, the volume fractions, and the incident angles, basedupon said plurality of models; and an analyzing step 1C-3 for selectinga model which exhibits the minimal mean square error (χ²), or a model,of which said film thicknesses, said volume fractions, and said incidentangles, are within predetermined ranges, and which exhibit the minimalmean square error (χ²), from the fitting results obtained in saidanalyzing step 1C-2.
 18. A thin-film triple-layer-structure measurementor thin-film multi-layer-structure measurement method for analyzingspectroscopic data acquired from a spectroscopic ellipsometer accordingto any one of claims 11 through 14, wherein said analyzing stage 2C-1includes: an analyzing step 2C-1-1 for replacing the optical constantsof the layer of interest with a single dispersion formula, which is theleast known in said thin-film triple-layer structure or thin-filmn-layer structure, in said determined initial model; an analyzing step2C-1-2 for forming a plurality of models based upon said initial modelwith the film thicknesses, the volume fractions, or the like, of desiredlayers other than said layer of interest (the number of layers is 1through (n−1)), as parameters, and performing EBLMC for said layer ofinterest based upon each model; an analyzing step 2C-1-3 for selecting amodel which exhibit the minimal mean square error (χ²), or a model, ofwhich said film thicknesses, said volume fractions, said parameters ofthe dispersion formula, and said incident angle, are withinpredetermined ranges, and which exhibit the minimal mean square error(χ²), from the fitting results using EBLMC, obtained in said analyzingstep 2C-1-2.
 19. A thin-film triple-layer-structure measurement orthin-film multi-layer-structure measurement method for analyzingspectroscopic data acquired from a spectroscopic ellipsometer accordingto any one of claims 11 through 14, wherein in each of analyzing stage2C-2 through 2C-t, the same steps as said analyzing step 2C-1-1 throughanalyzing step 2C-1 described in claim 18 are performed, making anassumption that the optical constants of the layer of interest obtainedin the previous stage are almost known.
 20. A thin-filmtriple-layer-structure measurement or thin-film multi-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer according to any one of claims 11 through 14,wherein in said analyzing phase 2C, EBLMC is performed for the materialsforming said triple-layer structure or n-layer structure in order ofuncertainty of the optical constants of said materials, and wherein saidEBLMC is performed for at least one to t times, regardless of the numberof the layers in said structure.
 21. A thin-film triple-layer-structuremeasurement or thin-film multi-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometeraccording to any one of claims 11 through 14, wherein in said analyzingphase 2C, in the event that the fitting results with the minimal meansquare error (χ²) do not exhibit said film thicknesses, said parametersof the dispersion formula, said volume fractions, and said incidentangle, within predetermined ranges, said analyzing phase 2C is repeatedwith a certain number of iterations.
 22. A thin-filmtriple-layer-structure measurement or thin-film multi-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer according to claim 12 or claim 14, wherein insaid analyzing phase 3C, the final fitting is performed for desiredparameters of the model obtained said analyzing phase 2C, confirmationis made for the fitting results obtained in said final fitting, and saidfitting results are stored.
 23. A thin-film triple-layer-structuremeasurement or thin-film multi-layer-structure measurement method foranalyzing spectroscopic data acquired from a spectroscopic ellipsometeraccording to claim 12 or claim 14, wherein in the event thatconfirmation is made in said analyzing step 3C-2 that the fittingresults with the minimal mean square error (χ²) obtained in saidanalyzing step 3C-1 are not within predetermined ranges, the flowreturns to said analyzing phase 1C, and analysis is made again.
 24. Athin-film triple-layer-structure measurement or thin-filmmulti-layer-structure measurement method for analyzing spectroscopicdata acquired from a spectroscopic ellipsometer according to any one ofclaims 11 through 14, wherein said analyzing stage 2C-1 includes: ananalyzing step 2C-1-1 wherein in the event that the layer of interestcannot be represented by a single dispersion formula in the same way asin claim 18, Effective Medium Approximation (EMA) is performed making anassumption that said layer of interest is formed of a mixture of severalmaterials, and at least one material forming” said layer of interest isrepresented by a dispersion formula; an analyzing step 2C-1-2 forforming multiple models with film thicknesses or volume fractions ofdesired layers 1 through (n−1) (n denotes the number of layers of saidstructure) other than said layer of interest, as parameters andperforming EBLMC for said layer of interest for each model whilechanging the volume fraction thereof as a parameter.
 25. A thin-filmtriple-layer-structure measurement or thin-film multi-layer-structuremeasurement method for analyzing spectroscopic data acquired from aspectroscopic ellipsometer according to any one of claims 11 through 14,further comprising: a spectroscopic measurement phase wherein incidentlight is cast onto a triple-layer-structure or multi-layer-structure ona substrate which is to be measured while changing the wavelength of theincident light as a parameter in order to obtain the ψ_(E) and Δ_(E)spectrums, i.e., the ψ_(E)(λ_(i)) and Δ_(E)(λ_(i)) for each wavelengthλ_(i), which represent the change in polarization between the incidentlight and the reflected light; an analyzing step for assuming aplurality of measurement conditions (Zi) in a plausible range andperforming processing from said analyzing step 1C or analyzing step 1C-1through 2C-t-3 for each assumed measurement condition (Zi); and ananalyzing step 1C-4 or 2C-t-4 for selecting fitting results, whichexhibit the minimal mean square error (χ²), or the parameters of thedispersion formula, the volume fraction, and the incident angle, arewithin a predetermined range, and which exhibit the minimal mean squareerror (χ²) which are selected from the fitting results obtained in saidanalyzing step.
 26. A thin-film triple-layer-structure measurement orthin-film multi-layer-structure measurement method for analyzingspectroscopic data acquired from a spectroscopic ellipsometer accordingto any one of claims 11 through 14, wherein in each of said steps forselecting the results which exhibit the least difference, described insaid analyzing phases 1C, 2C, and 3C, the mean square error (χ²) areobtained between the fitting results and the measured values, and thefitting results which exhibit the minimal mean square error (χ²), or thefitting results, of which the film thicknesses, the parameters of thedispersion formula, the volume fraction, and the change in the incidentangle, are within predetermined ranges, and which exhibit the minimalmean square error (χ²), are selected.